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ស៊ីនុស - វិគីភីឌា
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class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=km" class=""><span>បរិច្ចាគ</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%94%E1%9E%84%E1%9F%92%E1%9E%80%E1%9E%BE%E1%9E%8F%E1%9E%82%E1%9E%8E%E1%9E%93%E1%9E%B8&returnto=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តបង្កើតគណនីនិងកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។" class=""><span>បង្កើតគណនី</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%80%E1%9E%8F%E1%9F%8B%E1%9E%88%E1%9F%92%E1%9E%98%E1%9F%84%E1%9F%87%E1%9E%85%E1%9E%BC%E1%9E%9B%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%A2%E1%9F%92%E1%9E%93%E1%9E%80%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%BE%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9F%E1%9F%8B&returnto=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តឱ្យកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។ [o]" accesskey="o" class=""><span>កត់ឈ្មោះចូល</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="ជម្រើសផ្សេងទៀត" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="ឧបករណ៍ផ្ទាល់ខ្លួន" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">ឧបករណ៍ផ្ទាល់ខ្លួន</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="បញ្ជីសម្រាប់អ្នកប្រើប្រាស់" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=km"><span>បរិច្ចាគ</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%94%E1%9E%84%E1%9F%92%E1%9E%80%E1%9E%BE%E1%9E%8F%E1%9E%82%E1%9E%8E%E1%9E%93%E1%9E%B8&returnto=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តបង្កើតគណនីនិងកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>បង្កើតគណនី</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%80%E1%9E%8F%E1%9F%8B%E1%9E%88%E1%9F%92%E1%9E%98%E1%9F%84%E1%9F%87%E1%9E%85%E1%9E%BC%E1%9E%9B%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%A2%E1%9F%92%E1%9E%93%E1%9E%80%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%BE%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9F%E1%9F%8B&returnto=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តឱ្យកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>កត់ឈ្មោះចូល</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> ទំព័រសម្រាប់អ្នកកែសម្រួលដែលបានកត់ឈ្មោះចេញ <a href="/wiki/%E1%9E%87%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%99:Introduction" aria-label="ស្វែងយល់បន្ថែមអំពីការកែសម្រួល"><span>ស្វែងយល់បន្ថែម</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%9A%E1%9E%BD%E1%9E%98%E1%9E%85%E1%9F%86%E1%9E%8E%E1%9F%82%E1%9E%80%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%81%E1%9F%92%E1%9E%89%E1%9E%BB%E1%9F%86" title="បញ្ជីកំណែប្រែធ្វើឡើងពីអាសយដ្ឋាន IP នេះ [y]" accesskey="y"><span>ការរួមចំណែក</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%96%E1%9E%B7%E1%9E%97%E1%9E%B6%E1%9E%80%E1%9F%92%E1%9E%9F%E1%9E%B6%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%81%E1%9F%92%E1%9E%89%E1%9E%BB%E1%9F%86" title="ការពិភាក្សាអំពីកំណែប្រែដែលធ្វើឡើងចេញពីអាសយដ្ឋាន IP នេះ [n]" accesskey="n"><span>ការពិភាក្សា</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eលាក់\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv 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<div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">មាតិកា</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ប្ដូរទីតាំងទៅរបារចំហៀង</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">លាក់</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">ក្បាលទំព័រ</div> </a> </li> <li id="toc-និយមន័យ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#និយមន័យ"> <div class="vector-toc-text"> <span class="vector-toc-numb">១</span> <span>និយមន័យ</span> </div> </a> <button aria-controls="toc-និយមន័យ-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle និយមន័យ subsection</span> </button> <ul id="toc-និយមន័យ-sublist" class="vector-toc-list"> <li id="toc-ក្នុងត្រីកោណកែង" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ក្នុងត្រីកោណកែង"> <div class="vector-toc-text"> <span class="vector-toc-numb">១.១</span> <span>ក្នុងត្រីកោណកែង</span> </div> </a> <ul id="toc-ក្នុងត្រីកោណកែង-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ក្នុងកូអរដោនេប៉ូលែរ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ក្នុងកូអរដោនេប៉ូលែរ"> <div class="vector-toc-text"> <span class="vector-toc-numb">១.២</span> <span>ក្នុងកូអរដោនេប៉ូលែរ</span> </div> </a> <ul id="toc-ក្នុងកូអរដោនេប៉ូលែរ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ក្នុងរង្វង់ត្រីកោណមាត្រ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ក្នុងរង្វង់ត្រីកោណមាត្រ"> <div class="vector-toc-text"> <span class="vector-toc-numb">១.៣</span> <span>ក្នុងរង្វង់ត្រីកោណមាត្រ</span> </div> </a> <ul id="toc-ក្នុងរង្វង់ត្រីកោណមាត្រ-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ពន្លាតជាស៊េរី" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ពន្លាតជាស៊េរី"> <div class="vector-toc-text"> <span class="vector-toc-numb">២</span> <span>ពន្លាតជាស៊េរី</span> </div> </a> <ul id="toc-ពន្លាតជាស៊េរី-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ក្រាប" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ក្រាប"> <div class="vector-toc-text"> <span class="vector-toc-numb">៣</span> <span>ក្រាប</span> </div> </a> <ul id="toc-ក្រាប-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-រូបមន្ត" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#រូបមន្ត"> <div class="vector-toc-text"> <span class="vector-toc-numb">៤</span> <span>រូបមន្ត</span> </div> </a> <ul id="toc-រូបមន្ត-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-អាំងតេក្រាលដែលមានស៊ីនុស" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#អាំងតេក្រាលដែលមានស៊ីនុស"> <div class="vector-toc-text"> <span class="vector-toc-numb">៥</span> <span>អាំងតេក្រាលដែលមានស៊ីនុស</span> </div> </a> <ul id="toc-អាំងតេក្រាលដែលមានស៊ីនុស-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-តំលៃពិសេស" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#តំលៃពិសេស"> <div class="vector-toc-text"> <span class="vector-toc-numb">៦</span> <span>តំលៃពិសេស</span> </div> </a> <ul id="toc-តំលៃពិសេស-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ទ្រឹស្តីបទស៊ីនុស" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ទ្រឹស្តីបទស៊ីនុស"> <div class="vector-toc-text"> <span class="vector-toc-numb">៧</span> <span>ទ្រឹស្តីបទស៊ីនុស</span> </div> </a> <ul id="toc-ទ្រឹស្តីបទស៊ីនុស-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="មាតិកា" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of 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</div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" 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href="/wiki/%E1%9E%A2%E1%9E%93%E1%9E%BB%E1%9E%82%E1%9E%98%E1%9E%93%E1%9F%8D%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A" title="អនុគមន៍ត្រីកោណមាត្រ">អនុគមន៍ត្រីកោណមាត្រ</a>គ្រឹះ។ តំលៃនៃអនុគមន៍ស៊ីនុសក្នុងដែនកំនត់ពិតគឺស្ថិតនៅចន្លោះ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ [-1,1]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">[</mo> <mo>−<!-- − --></mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ [-1,1]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3175907f761b9e16bc6c405d2b521caa35e8062d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.041ex; height:2.843ex;" alt="{\displaystyle \ [-1,1]}"></span> ។ ស៊ីនុសជា<a href="/w/index.php?title=%E1%9E%A2%E1%9E%93%E1%9E%BB%E1%9E%82%E1%9E%98%E1%9E%93%E1%9F%8D%E1%9E%81%E1%9E%BD%E1%9E%94&action=edit&redlink=1" class="new" title="អនុគមន៍ខួប (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">អនុគមន៍ខួប</a>ដែលមានខួបស្មើនឹង <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>2</mn> <mi>π<!-- π --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/685e78ce3c69cf9cc2e1330f60f80e5beb6029c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.075ex; height:2.176ex;" alt="{\displaystyle \ 2\pi }"></span> ។ ចំពោះអាគុយម់ង់ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\frac {(4n+1)\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>π<!-- π --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\frac {(4n+1)\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc4e9f451cb3ed8167f462a98f9b94dc93f4bf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.118ex; height:5.676ex;" alt="{\displaystyle \ {\frac {(4n+1)\pi }{2}}}"></span> (ដែល n ជាចំនួនគត់) អនុគមន៍មានតំលៃធំបំផុតស្មើនឹង ១ ។ ចំពោះអាគុយម៉ង់ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\frac {(4n+3)\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mi>π<!-- π --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\frac {(4n+3)\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b75f3a23b8aa37fa36fbd8e0f705bd18ef04e8c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.118ex; height:5.676ex;" alt="{\displaystyle \ {\frac {(4n+3)\pi }{2}}}"></span> អនុគមន៍មានតំលៃតូចបំផុតស្មើនឹង − ១ ។ </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%E1%9E%AF%E1%9E%80%E1%9E%9F%E1%9E%B6%E1%9E%9A:Sin_drawing_process.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Sin_drawing_process.gif/400px-Sin_drawing_process.gif" decoding="async" width="400" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Sin_drawing_process.gif/600px-Sin_drawing_process.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7d/Sin_drawing_process.gif 2x" data-file-width="711" data-file-height="249" /></a><figcaption>ដំណើរនៃក្រាបនៃអនុគមន៍ស៊ីនុស y = sin x (x គិតជារ៉ាដ្យង់) ដោយប្រើ<a href="/w/index.php?title=%E1%9E%9A%E1%9E%84%E1%9F%92%E1%9E%9C%E1%9E%84%E1%9F%8B%E2%80%8B%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A&action=edit&redlink=1" class="new" title="រង្វង់ត្រីកោណមាត្រ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">រង្វង់ត្រីកោណមាត្រ</a></figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="និយមន័យ"><span id=".E1.9E.93.E1.9E.B7.E1.9E.99.E1.9E.98.E1.9E.93.E1.9F.90.E1.9E.99"></span>និយមន័យ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=1" title="កែប្រែផ្នែក៖ និយមន័យ"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="ក្នុងត្រីកោណកែង"><span id=".E1.9E.80.E1.9F.92.E1.9E.93.E1.9E.BB.E1.9E.84.E1.9E.8F.E1.9F.92.E1.9E.9A.E1.9E.B8.E1.9E.80.E1.9F.84.E1.9E.8E.E1.9E.80.E1.9F.82.E1.9E.84"></span>ក្នុង<a href="/wiki/%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%80%E1%9F%82%E1%9E%84" title="ត្រីកោណកែង">ត្រីកោណកែង</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=2" title="កែប្រែផ្នែក៖ ក្នុងត្រីកោណកែង"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/%E1%9E%AF%E1%9E%80%E1%9E%9F%E1%9E%B6%E1%9E%9A:Triangle_ratio.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/km/thumb/8/84/Triangle_ratio.png/250px-Triangle_ratio.png" decoding="async" width="250" height="281" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/km/thumb/8/84/Triangle_ratio.png/375px-Triangle_ratio.png 1.5x, //upload.wikimedia.org/wikipedia/km/8/84/Triangle_ratio.png 2x" data-file-width="481" data-file-height="541" /></a><figcaption></figcaption></figure> <p>ស៊ីនុសនៃមុំមួយ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>θ<!-- θ --></mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bff010a979f4ef4f3e5b38407e5ce1930a29a38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.48ex; height:2.843ex;" alt="{\displaystyle \ (\theta )}"></span> គឺជាផលធៀបរវាងរង្វាស់ប្រវែងនៃជ្រុងឈម និង រង្វាស់<a href="/wiki/%E1%9E%A2%E1%9F%8A%E1%9E%B8%E1%9E%94%E1%9F%89%E1%9E%BC%E1%9E%8F%E1%9F%81%E1%9E%93%E1%9E%BB%E1%9E%9F" title="អ៊ីប៉ូតេនុស">អ៊ីប៉ូតេនុស</a>។ យើងតាង </p> <ul><li>អ៊ីប៉ូតេនុស (AC) ដោយ<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8eb515077d0b969895a7e62dfe0ae6a198e2426f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.92ex; height:2.176ex;" alt="{\displaystyle \ h}"></span></li> <li>ជ្រុងឈម (BC) ដោយ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a14b4bc0b189c2d21060cd9ed1516a1f7e707c85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.81ex; height:1.676ex;" alt="{\displaystyle \ a}"></span></li></ul> <p>យើងបាន </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta ={\frac {BC}{AC}}={\frac {a}{h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>h</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta ={\frac {BC}{AC}}={\frac {a}{h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/107bec0311dee88690311263fa519be558bd47f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.072ex; height:5.509ex;" alt="{\displaystyle \sin \theta ={\frac {BC}{AC}}={\frac {a}{h}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="ក្នុងកូអរដោនេប៉ូលែរ"><span id=".E1.9E.80.E1.9F.92.E1.9E.93.E1.9E.BB.E1.9E.84.E2.80.8B.E1.9E.80.E1.9E.BC.E1.9E.A2.E1.9E.9A.E1.9E.8A.E1.9F.84.E1.9E.93.E1.9F.81.E1.9E.94.E1.9F.89.E1.9E.BC.E1.9E.9B.E1.9F.82.E1.9E.9A"></span>ក្នុង<a href="/w/index.php?title=%E1%9E%80%E1%9E%BC%E1%9E%A2%E1%9E%9A%E1%9E%8A%E1%9F%84%E1%9E%93%E1%9F%81%E1%9E%94%E1%9F%89%E1%9E%BC%E1%9E%9B%E1%9F%82%E1%9E%9A&action=edit&redlink=1" class="new" title="កូអរដោនេប៉ូលែរ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">កូអរដោនេប៉ូលែរ</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=3" title="កែប្រែផ្នែក៖ ក្នុងកូអរដោនេប៉ូលែរ"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \alpha ={\frac {y}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>α<!-- α --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha ={\frac {y}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c90eb839a98497f7ff314682b9befa523942933e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.82ex; height:4.843ex;" alt="{\displaystyle \sin \alpha ={\frac {y}{r}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="ក្នុងរង្វង់ត្រីកោណមាត្រ"><span id=".E1.9E.80.E1.9F.92.E1.9E.93.E1.9E.BB.E1.9E.84.E2.80.8B.E1.9E.9A.E1.9E.84.E1.9F.92.E1.9E.9C.E1.9E.84.E1.9F.8B.E1.9E.8F.E1.9F.92.E1.9E.9A.E1.9E.B8.E1.9E.80.E1.9F.84.E1.9E.8E.E1.9E.98.E1.9E.B6.E1.9E.8F.E1.9F.92.E1.9E.9A"></span>ក្នុង<a href="/wiki/%E1%9E%9A%E1%9E%84%E1%9F%92%E1%9E%9C%E1%9E%84%E1%9F%8B%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A" title="រង្វង់ត្រីកោណមាត្រ">រង្វង់ត្រីកោណមាត្រ</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=4" title="កែប្រែផ្នែក៖ ក្នុងរង្វង់ត្រីកោណមាត្រ"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="ពន្លាតជាស៊េរី"><span id=".E1.9E.96.E1.9E.93.E1.9F.92.E1.9E.9B.E1.9E.B6.E1.9E.8F.E1.9E.87.E1.9E.B6.E1.9E.9F.E1.9F.8A.E1.9F.81.E1.9E.9A.E1.9E.B8"></span>ពន្លាតជាស៊េរី</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=5" title="កែប្រែផ្នែក៖ ពន្លាតជាស៊េរី"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ពន្លាតជា<a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9F%81%E1%9E%9A%E1%9E%B8%E1%9E%8F%E1%9F%81%E1%9E%9B%E1%9F%90%E1%9E%9A&action=edit&redlink=1" class="new" title="ស៊េរីតេល័រ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">ស៊េរីតេល័រ</a>នៃអនុគមន៍ស៊ីនុស៖ </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots +{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>5</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mn>7</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯<!-- ⋯ --></mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mo>−<!-- − --></mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots +{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd3a3943b7f89af233e3528c13ab2d478c45d1bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:51.554ex; height:6.509ex;" alt="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots +{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mo>=</mo> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mo>−<!-- − --></mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a337ae90a13bc59ae4eff7c969b84b49aa8ab5ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.381ex; height:6.843ex;" alt="{\displaystyle \sin x=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}\;x^{2n+1}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="ក្រាប"><span id=".E1.9E.80.E1.9F.92.E1.9E.9A.E1.9E.B6.E1.9E.94"></span>ក្រាប</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=6" title="កែប្រែផ្នែក៖ ក្រាប"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/%E1%9E%AF%E1%9E%80%E1%9E%9F%E1%9E%B6%E1%9E%9A:Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg/700px-Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg.png" decoding="async" width="700" height="490" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg/1050px-Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg/1400px-Funci%C3%B3n_Trigonom%C3%A9trica_R100.svg.png 2x" data-file-width="1000" data-file-height="700" /></a><figcaption>ក្រាបនៃអនុគមន៍ត្រីកោណមាត្រក្នុងប្លង់ xy ដែលតំលៃនៅលើអ័ក្សអាប់ស៊ីសត្រូវនឹង <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π<!-- π --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> <a href="/w/index.php?title=%E1%9E%9A%E1%9F%89%E1%9E%B6%E1%9E%8A%E1%9F%92%E1%9E%99%E1%9E%84%E1%9F%8B&action=edit&redlink=1" class="new" title="រ៉ាដ្យង់ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">រ៉ាដ្យង់</a>ដងនៃតំលៃនោះ។ អនុគមន៍ស៊ីនុសត្រូវបានគេហៅថា[ស៊ីនុយសូអ៊ីត</figcaption></figure> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/%E1%9E%AF%E1%9E%80%E1%9E%9F%E1%9E%B6%E1%9E%9A:Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg/700px-Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg.png" decoding="async" width="700" height="490" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg/1050px-Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg/1400px-Funci%C3%B3n_Trigonom%C3%A9trica_S100.svg.png 2x" data-file-width="1000" data-file-height="700" /></a><figcaption>ក្រាបនៃអនុគមន៍ត្រីកោណមាត្រក្នុងប្លង់ xy ដែលតំលៃនៅលើអ័ក្សអាប់ស៊ីសគិតជា<a href="/w/index.php?title=%E1%9E%8A%E1%9E%BA%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9F%81&action=edit&redlink=1" class="new" title="ដឺក្រេ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">ដឺក្រេ</a></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="រូបមន្ត"><span id=".E1.9E.9A.E1.9E.BC.E1.9E.94.E1.9E.98.E1.9E.93.E1.9F.92.E1.9E.8F"></span>រូបមន្ត</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=7" title="កែប្រែផ្នែក៖ រូបមន្ត"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b>រូបមន្តបំលែងនៃស៊ីនុស</b></li></ul> <table class="wikitable" style="background-color:#FFFFFF;text-align:center"> <tbody><tr> <th>អនុគមន៍ </th> <th>sin </th> <th>cos </th> <th>tan </th> <th>csc </th> <th>sec </th> <th>cot </th></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85a567c5248097d657724e34cb8666208c3085ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.786ex; height:2.176ex;" alt="{\displaystyle \sin \theta =}"></span> </th> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24199033500a02f8fc7e410e959aa622f8fa3ed2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.914ex; height:2.176ex;" alt="{\displaystyle \sin \theta \ }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {1-\cos ^{2}\theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−<!-- − --></mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {1-\cos ^{2}\theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b825d54fdfbfc9eff6f525efabccace541f6955b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.97ex; height:3.509ex;" alt="{\displaystyle {\sqrt {1-\cos ^{2}\theta }}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\tan \theta }{\sqrt {1+\tan ^{2}\theta }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\tan \theta }{\sqrt {1+\tan ^{2}\theta }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55eb6456849e116e71c76d832ae05b8051816923" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.054ex; height:6.676ex;" alt="{\displaystyle {\frac {\tan \theta }{\sqrt {1+\tan ^{2}\theta }}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\csc \theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>csc</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\csc \theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fc4edd8913183d4072ff4afc02cae272602d49d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:5.295ex; height:5.343ex;" alt="{\displaystyle {\frac {1}{\csc \theta }}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {\sec ^{2}\theta -1}}{\sec \theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <msup> <mi>sec</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>−<!-- − --></mo> <mn>1</mn> </msqrt> <mrow> <mi>sec</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {\sec ^{2}\theta -1}}{\sec \theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f493a83afba5b4d2ca73d9c80a1235d59967b32c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.676ex; height:6.343ex;" alt="{\displaystyle {\frac {\sqrt {\sec ^{2}\theta -1}}{\sec \theta }}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\sqrt {1+\cot ^{2}\theta }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>cot</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\sqrt {1+\cot ^{2}\theta }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82e7642ece6a5d8db07485d76b5951b4ee2b297f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:12.794ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{\sqrt {1+\cot ^{2}\theta }}}}"></span> </td></tr></tbody></table> <ul><li><b>រូបមន្តស៊ីនុសនៃផលបូកនិងផលដករវាងមុំពីរ</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \left(x+y\right)=\sin x\cos y+\cos x\sin y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>y</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \left(x+y\right)=\sin x\cos y+\cos x\sin y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e863739245ff9022e0766723a53d52f05fc06017" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.156ex; height:2.843ex;" alt="{\displaystyle \sin \left(x+y\right)=\sin x\cos y+\cos x\sin y}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \left(x-y\right)=\sin x\cos y-\cos x\sin y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−<!-- − --></mo> <mi>y</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>y</mi> <mo>−<!-- − --></mo> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \left(x-y\right)=\sin x\cos y-\cos x\sin y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e881a8119150497d49cff66cd28e3bf03aa592d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.156ex; height:2.843ex;" alt="{\displaystyle \sin \left(x-y\right)=\sin x\cos y-\cos x\sin y}"></span></dd></dl> <ul><li><b>រូបមន្តមុំទ្វេដង</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(2\theta )=2\sin \theta \cos \theta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>θ<!-- θ --></mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(2\theta )=2\sin \theta \cos \theta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6d5b87ac4202617b5c32f9fecb5df26d0fdca5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.262ex; height:2.843ex;" alt="{\displaystyle \sin(2\theta )=2\sin \theta \cos \theta \,}"></span></dd></dl> <ul><li><b>រូបមន្តមុំបីដង</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin 3\theta =3\sin \theta -4\sin ^{3}\theta \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mn>3</mn> <mi>θ<!-- θ --></mi> <mo>=</mo> <mn>3</mn> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>−<!-- − --></mo> <mn>4</mn> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin 3\theta =3\sin \theta -4\sin ^{3}\theta \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe2b8785f6f7d9ad1c0c0d3efe15a26f1700ad80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:24.641ex; height:2.843ex;" alt="{\displaystyle \sin 3\theta =3\sin \theta -4\sin ^{3}\theta \,}"></span></dd></dl> <ul><li><b>រូបមន្តកន្លះមុំ</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin {\frac {\theta }{2}}=\pm \,{\sqrt {\frac {1-\cos \theta }{2}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>θ<!-- θ --></mi> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mo>±<!-- ± --></mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> <mn>2</mn> </mfrac> </msqrt> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin {\frac {\theta }{2}}=\pm \,{\sqrt {\frac {1-\cos \theta }{2}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4940ff945546ae005d5af0d36e79767d20de3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.674ex; height:6.343ex;" alt="{\displaystyle \sin {\frac {\theta }{2}}=\pm \,{\sqrt {\frac {1-\cos \theta }{2}}}\,}"></span></dd></dl> <ul><li><b>រូបមន្តផលបូកនិងផលដកស៊ីនុស</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta +\sin \phi =2\sin \left({\frac {\theta +\phi }{2}}\right)\cos \left({\frac {\theta -\phi }{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>+</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>ϕ<!-- ϕ --></mi> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>θ<!-- θ --></mi> <mo>+</mo> <mi>ϕ<!-- ϕ --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>θ<!-- θ --></mi> <mo>−<!-- − --></mo> <mi>ϕ<!-- ϕ --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta +\sin \phi =2\sin \left({\frac {\theta +\phi }{2}}\right)\cos \left({\frac {\theta -\phi }{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81fbad7cfdaa0650b1a778599b23df0931386fed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:41.951ex; height:6.176ex;" alt="{\displaystyle \sin \theta +\sin \phi =2\sin \left({\frac {\theta +\phi }{2}}\right)\cos \left({\frac {\theta -\phi }{2}}\right)}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta -\sin \phi =2\cos \left({\theta +\phi \over 2}\right)\sin \left({\theta -\phi \over 2}\right)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>−<!-- − --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>ϕ<!-- ϕ --></mi> <mo>=</mo> <mn>2</mn> <mi>cos</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>θ<!-- θ --></mi> <mo>+</mo> <mi>ϕ<!-- ϕ --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>θ<!-- θ --></mi> <mo>−<!-- − --></mo> <mi>ϕ<!-- ϕ --></mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta -\sin \phi =2\cos \left({\theta +\phi \over 2}\right)\sin \left({\theta -\phi \over 2}\right)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06cc828415ae4edfd8f1e6b980ee355d015ac592" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:42.338ex; height:6.176ex;" alt="{\displaystyle \sin \theta -\sin \phi =2\cos \left({\theta +\phi \over 2}\right)\sin \left({\theta -\phi \over 2}\right)\,}"></span></dd></dl> <ul><li><b>រូបមន្តស៊ីនុសនិងតង់សង់កន្លះមុំ</b></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \alpha ={\frac {2\tan {\frac {\alpha }{2}}}{1+\tan ^{2}{\frac {\alpha }{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>α<!-- α --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>tan</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α<!-- α --></mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α<!-- α --></mi> <mn>2</mn> </mfrac> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha ={\frac {2\tan {\frac {\alpha }{2}}}{1+\tan ^{2}{\frac {\alpha }{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4331d15e171566984437fa575f9b984b17f4507" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:19.357ex; height:7.343ex;" alt="{\displaystyle \sin \alpha ={\frac {2\tan {\frac {\alpha }{2}}}{1+\tan ^{2}{\frac {\alpha }{2}}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="អាំងតេក្រាលដែលមានស៊ីនុស"><span id=".E1.9E.A2.E1.9E.B6.E1.9F.86.E1.9E.84.E1.9E.8F.E1.9F.81.E1.9E.80.E1.9F.92.E1.9E.9A.E1.9E.B6.E1.9E.9B.E2.80.8B.E1.9E.8A.E1.9F.82.E1.9E.9B.E2.80.8B.E1.9E.98.E1.9E.B6.E1.9E.93.E2.80.8B.E1.9E.9F.E1.9F.8A.E1.9E.B8.E1.9E.93.E1.9E.BB.E1.9E.9F"></span>អាំងតេក្រាលដែលមានស៊ីនុស</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=8" title="កែប្រែផ្នែក៖ អាំងតេក្រាលដែលមានស៊ីនុស"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin cx\;dx=-{\frac {1}{c}}\cos cx\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin cx\;dx=-{\frac {1}{c}}\cos cx\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90927a9524ca2ebb7532b3b642442416f997074c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:24.865ex; height:5.676ex;" alt="{\displaystyle \int \sin cx\;dx=-{\frac {1}{c}}\cos cx\,\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \ |sinx|\,dx=-\cos x\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \ |sinx|\,dx=-\cos x\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a8d30743e07ec017218974060124a3e352ba85c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:22.514ex; height:5.676ex;" alt="{\displaystyle \int \ |sinx|\,dx=-\cos x\,\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin ^{n}{cx}\;dx=-{\frac {\sin ^{n-1}cx\cos cx}{nc}}+{\frac {n-1}{n}}\int \sin ^{n-2}cx\;dx\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>x</mi> </mrow> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>∫<!-- ∫ --></mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin ^{n}{cx}\;dx=-{\frac {\sin ^{n-1}cx\cos cx}{nc}}+{\frac {n-1}{n}}\int \sin ^{n-2}cx\;dx\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe66897c2f5772a0df0c2888e699f9a4d9e80db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:57.95ex; height:6.176ex;" alt="{\displaystyle \int \sin ^{n}{cx}\;dx=-{\frac {\sin ^{n-1}cx\cos cx}{nc}}+{\frac {n-1}{n}}\int \sin ^{n-2}cx\;dx\,\!}"></span><span style="white-space:nowrap;">   </span> (ចំពោះ<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ n>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>n</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ n>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04c6d45911d4c6078160a691fb3ee7f6bc15a14c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.236ex; height:2.176ex;" alt="{\displaystyle \ n>0}"></span> )</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin ^{2}{cx}\;dx={\frac {x}{2}}-{\frac {1}{4c}}\sin 2cx={\frac {x}{2}}-{\frac {1}{2c}}\sin cx\cos cx\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>x</mi> </mrow> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mi>c</mi> </mrow> </mfrac> </mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mn>2</mn> <mi>c</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> </mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin ^{2}{cx}\;dx={\frac {x}{2}}-{\frac {1}{4c}}\sin 2cx={\frac {x}{2}}-{\frac {1}{2c}}\sin cx\cos cx\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e299cc3a3d71b32d9a94abc0a2d8bdddfc7702c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.271ex; width:53.826ex; height:5.676ex;" alt="{\displaystyle \int \sin ^{2}{cx}\;dx={\frac {x}{2}}-{\frac {1}{4c}}\sin 2cx={\frac {x}{2}}-{\frac {1}{2c}}\sin cx\cos cx\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\sqrt {1-\sin {x}}}\,dx=\int {\sqrt {\operatorname {cvs} {x}}}\,dx=2{\frac {\cos {\frac {x}{2}}+\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}-\sin {\frac {x}{2}}}}{\sqrt {\operatorname {cvs} {x}}}=2{\sqrt {1+\sin {x}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−<!-- − --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msqrt> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>cvs</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msqrt> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>cvs</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msqrt> </mrow> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\sqrt {1-\sin {x}}}\,dx=\int {\sqrt {\operatorname {cvs} {x}}}\,dx=2{\frac {\cos {\frac {x}{2}}+\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}-\sin {\frac {x}{2}}}}{\sqrt {\operatorname {cvs} {x}}}=2{\sqrt {1+\sin {x}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/644e701f7bfac6170be097c4eda7308c9c8ec26e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:71.297ex; height:7.176ex;" alt="{\displaystyle \int {\sqrt {1-\sin {x}}}\,dx=\int {\sqrt {\operatorname {cvs} {x}}}\,dx=2{\frac {\cos {\frac {x}{2}}+\sin {\frac {x}{2}}}{\cos {\frac {x}{2}}-\sin {\frac {x}{2}}}}{\sqrt {\operatorname {cvs} {x}}}=2{\sqrt {1+\sin {x}}}}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int x\sin cx\;dx={\frac {\sin cx}{c^{2}}}-{\frac {x\cos cx}{c}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mi>x</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int x\sin cx\;dx={\frac {\sin cx}{c^{2}}}-{\frac {x\cos cx}{c}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ba196bb420de05f3a536e722b9fa9b633ae1edb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:34.197ex; height:5.676ex;" alt="{\displaystyle \int x\sin cx\;dx={\frac {\sin cx}{c^{2}}}-{\frac {x\cos cx}{c}}\,\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int x^{n}\sin cx\;dx=-{\frac {x^{n}}{c}}\cos cx+{\frac {n}{c}}\int x^{n-1}\cos cx\;dx\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mi>c</mi> </mfrac> </mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>c</mi> </mfrac> </mrow> <mo>∫<!-- ∫ --></mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int x^{n}\sin cx\;dx=-{\frac {x^{n}}{c}}\cos cx+{\frac {n}{c}}\int x^{n-1}\cos cx\;dx\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d24c7c92628376a7de80f1d2d1d9fd90f88b483" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:51.286ex; height:5.676ex;" alt="{\displaystyle \int x^{n}\sin cx\;dx=-{\frac {x^{n}}{c}}\cos cx+{\frac {n}{c}}\int x^{n-1}\cos cx\;dx\,\!}"></span> <span style="white-space:nowrap;">   </span> (ចំពោះ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ n>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>n</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ n>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04c6d45911d4c6078160a691fb3ee7f6bc15a14c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.236ex; height:2.176ex;" alt="{\displaystyle \ n>0}"></span> )</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\sin ^{2}{\frac {n\pi x}{a}}\;dx={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−<!-- − --></mo> <mi>a</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mn>2</mn> </mfrac> </mrow> </msubsup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>π<!-- π --></mi> <mi>x</mi> </mrow> <mi>a</mi> </mfrac> </mrow> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−<!-- − --></mo> <mn>6</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>24</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\sin ^{2}{\frac {n\pi x}{a}}\;dx={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1528fd4191273427972e6706fa41915d1032a45f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; margin-right: -0.387ex; width:37.032ex; height:7.509ex;" alt="{\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\sin ^{2}{\frac {n\pi x}{a}}\;dx={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\,\!}"></span><span style="white-space:nowrap;">   </span> (ចំពោះ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=2,4,6\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>6</mn> <mo>⋯<!-- ⋯ --></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=2,4,6\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f9499fd68222cb7978a873f9f7e96bf763d09cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.159ex; height:2.509ex;" alt="{\displaystyle n=2,4,6\cdots }"></span>)</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {\sin cx}{x}}dx=\sum _{i=0}^{\infty }(-1)^{i}{\frac {(cx)^{2i+1}}{(2i+1)\cdot (2i+1)!}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <mi>x</mi> </mfrac> </mrow> <mi>d</mi> <mi>x</mi> <mo>=</mo> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−<!-- − --></mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {\sin cx}{x}}dx=\sum _{i=0}^{\infty }(-1)^{i}{\frac {(cx)^{2i+1}}{(2i+1)\cdot (2i+1)!}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4c679a50c11f75c5624254025badb770884691f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:42.678ex; height:7.009ex;" alt="{\displaystyle \int {\frac {\sin cx}{x}}dx=\sum _{i=0}^{\infty }(-1)^{i}{\frac {(cx)^{2i+1}}{(2i+1)\cdot (2i+1)!}}\,\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {\sin cx}{x^{n}}}dx=-{\frac {\sin cx}{(n-1)x^{n-1}}}+{\frac {c}{n-1}}\int {\frac {\cos cx}{x^{n-1}}}dx\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mfrac> </mrow> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mfrac> </mrow> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {\sin cx}{x^{n}}}dx=-{\frac {\sin cx}{(n-1)x^{n-1}}}+{\frac {c}{n-1}}\int {\frac {\cos cx}{x^{n-1}}}dx\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee2c4bcf48fc3ff6ee0d8eb14b330bf55dacd67f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.387ex; width:50.785ex; height:6.009ex;" alt="{\displaystyle \int {\frac {\sin cx}{x^{n}}}dx=-{\frac {\sin cx}{(n-1)x^{n-1}}}+{\frac {c}{n-1}}\int {\frac {\cos cx}{x^{n-1}}}dx\,\!}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{\sin cx}}={\frac {1}{c}}\ln \left|\tan {\frac {cx}{2}}\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow> <mo>|</mo> <mrow> <mi>tan</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{\sin cx}}={\frac {1}{c}}\ln \left|\tan {\frac {cx}{2}}\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33e9b1d708e4a982d400c2bf4ce60212c69b1273" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.633ex; height:5.843ex;" alt="{\displaystyle \int {\frac {dx}{\sin cx}}={\frac {1}{c}}\ln \left|\tan {\frac {cx}{2}}\right|}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{\sin ^{n}cx}}={\frac {\cos cx}{c(1-n)\sin ^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\sin ^{n-2}cx}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> <mrow> <mi>c</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−<!-- − --></mo> <mi>n</mi> <mo stretchy="false">)</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>2</mn> </mrow> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{\sin ^{n}cx}}={\frac {\cos cx}{c(1-n)\sin ^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\sin ^{n-2}cx}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd1b9763f7dee6d588f49dc5fd2fadb70859a4f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-right: -0.387ex; width:53.812ex; height:6.343ex;" alt="{\displaystyle \int {\frac {dx}{\sin ^{n}cx}}={\frac {\cos cx}{c(1-n)\sin ^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\sin ^{n-2}cx}}\,\!}"></span> <span style="white-space:nowrap;">   </span> (ចំពោះ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ n>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>n</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ n>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2b5b9b1a7d5d90a254fc84b283091e8a2f162fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.236ex; height:2.176ex;" alt="{\displaystyle \ n>1}"></span>)</li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{1\pm \sin cx}}={\frac {1}{c}}\tan \left({\frac {cx}{2}}\mp {\frac {\pi }{4}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>±<!-- ± --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mi>tan</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>∓<!-- ∓ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{1\pm \sin cx}}={\frac {1}{c}}\tan \left({\frac {cx}{2}}\mp {\frac {\pi }{4}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce341569f2cd1bf50b4d093c9a4a5c6f236505ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.799ex; height:5.843ex;" alt="{\displaystyle \int {\frac {dx}{1\pm \sin cx}}={\frac {1}{c}}\tan \left({\frac {cx}{2}}\mp {\frac {\pi }{4}}\right)}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {x\;dx}{1+\sin cx}}={\frac {x}{c}}\tan \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)+{\frac {2}{c^{2}}}\ln \left|\cos \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>c</mi> </mfrac> </mrow> <mi>tan</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow> <mo>|</mo> <mrow> <mi>cos</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {x\;dx}{1+\sin cx}}={\frac {x}{c}}\tan \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)+{\frac {2}{c^{2}}}\ln \left|\cos \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2ad92be2fe75f28b3a47ea3948950df8e6efcb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:56.392ex; height:5.843ex;" alt="{\displaystyle \int {\frac {x\;dx}{1+\sin cx}}={\frac {x}{c}}\tan \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)+{\frac {2}{c^{2}}}\ln \left|\cos \left({\frac {cx}{2}}-{\frac {\pi }{4}}\right)\right|}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {x\;dx}{1-\sin cx}}={\frac {x}{c}}\cot \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)+{\frac {2}{c^{2}}}\ln \left|\sin \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>c</mi> </mfrac> </mrow> <mi>cot</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow> <mo>|</mo> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {x\;dx}{1-\sin cx}}={\frac {x}{c}}\cot \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)+{\frac {2}{c^{2}}}\ln \left|\sin \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57b478db3bb323ac13e34688e726f9c5b72fb44d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:55.877ex; height:5.843ex;" alt="{\displaystyle \int {\frac {x\;dx}{1-\sin cx}}={\frac {x}{c}}\cot \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)+{\frac {2}{c^{2}}}\ln \left|\sin \left({\frac {\pi }{4}}-{\frac {cx}{2}}\right)\right|}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {\sin cx\;dx}{1\pm \sin cx}}=\pm x+{\frac {1}{c}}\tan \left({\frac {\pi }{4}}\mp {\frac {cx}{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>±<!-- ± --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>c</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>±<!-- ± --></mo> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mi>tan</mi> <mo>⁡<!-- --></mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> <mo>∓<!-- ∓ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {\sin cx\;dx}{1\pm \sin cx}}=\pm x+{\frac {1}{c}}\tan \left({\frac {\pi }{4}}\mp {\frac {cx}{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0e1d0c0992f04eb68ac1d4b84f8c8fd96e43064" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:38.778ex; height:5.843ex;" alt="{\displaystyle \int {\frac {\sin cx\;dx}{1\pm \sin cx}}=\pm x+{\frac {1}{c}}\tan \left({\frac {\pi }{4}}\mp {\frac {cx}{2}}\right)}"></span></li></ul> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin c_{1}x\sin c_{2}x\;dx={\frac {\sin(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}-{\frac {\sin(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫<!-- ∫ --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>x</mi> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>x</mi> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin c_{1}x\sin c_{2}x\;dx={\frac {\sin(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}-{\frac {\sin(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42891b858dc548a7f3c390ceb990d55c328a19e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.387ex; width:53.338ex; height:6.509ex;" alt="{\displaystyle \int \sin c_{1}x\sin c_{2}x\;dx={\frac {\sin(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}-{\frac {\sin(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}\,\!}"></span> <span style="white-space:nowrap;">   </span> (ចំពោះ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ |c_{1}|\neq |c_{2}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≠<!-- ≠ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |c_{1}|\neq |c_{2}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/813b118a2aaee02734c1800a4c4ec2be7ab4ce88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.389ex; height:2.843ex;" alt="{\displaystyle \ |c_{1}|\neq |c_{2}|}"></span> )</li></ul> <div class="mw-heading mw-heading2"><h2 id="តំលៃពិសេស"><span id=".E1.9E.8F.E1.9F.86.E1.9E.9B.E1.9F.83.E1.9E.96.E1.9E.B7.E1.9E.9F.E1.9F.81.E1.9E.9F"></span>តំលៃពិសេស</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=9" title="កែប្រែផ្នែក៖ តំលៃពិសេស"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align: center;"> <tbody><tr> <th> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b1272b2462bfc7c89c80c80be3e3712829c8d6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.161ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{12}}}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da430867901fd359c000b52f2bd70b36cf5e2182" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{6}}}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f89d7c88c1c93dce69a46052a8e276e231063de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{4}}}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c83c684a603005cda4feb8eea0254143ffb0e16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{3}}}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {5\pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mi>π<!-- π --></mi> </mrow> <mn>12</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5\pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8e60a8a09f8e6c420879481acb6d8ead181e822" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.331ex; height:5.176ex;" alt="{\displaystyle {\frac {5\pi }{12}}}"></span> </th></tr> <tr> <td>sin </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78c627f0ebe511a980e4f73e69210a111a36bda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.873ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a11cfb2fdb143693b1daf78fcb5c11a023cb1c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fb9b5960bf5eae3065db9c23495e465f5fef61e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.934ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {2}}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {3}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {3}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4864a0c173339d1d88e89ca3c943f016744c879a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.934ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {3}}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b490d0765455c4d35af5b84445852edea3f2a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.873ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}}"></span> </td></tr></tbody></table> <table class="wikitable" style="text-align: center;"> <tbody><tr> <th><a href="/wiki/%E1%9E%98%E1%9E%BB%E1%9F%86" title="មុំ">មុំ</a> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd0e1e92cf5770c2bfbb1de8b4b7bf904c9deef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.217ex; height:2.343ex;" alt="{\displaystyle 0^{\circ }}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 30^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>30</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 30^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42f29df9c101d2a8dae3f1552342cfe4c3adb76c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 30^{\circ }}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 45^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>45</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 45^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28223ddedeb94a84bb15474cc64b5ce436cbe50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 45^{\circ }}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 60^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>60</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 60^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08c42292485b447b7f627a7accd90d5b439c11d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 60^{\circ }}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 90^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 90^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c326d317eddef3ad3e6625e018a708e290a039f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 90^{\circ }}"></span> </th></tr> <tr> <td>sin </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {0}}{2}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>0</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {0}}{2}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3086c0bfa8a66812641c2723b4a5de9b6d5400" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.195ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {0}}{2}}=0}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {1}}{2}}={1 \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>1</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {1}}{2}}={1 \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d01d5dcc0bfd57a8b66bad121aa02fe76e25c4b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.032ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {1}}{2}}={1 \over 2}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fb9b5960bf5eae3065db9c23495e465f5fef61e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.934ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {2}}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {3}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {3}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4864a0c173339d1d88e89ca3c943f016744c879a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.934ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {3}}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sqrt {4}}{2}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>4</mn> </msqrt> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {4}}{2}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4b38fd61be7c720b63d9f38552701eeb87ca4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.195ex; height:5.843ex;" alt="{\displaystyle {\frac {\sqrt {4}}{2}}=1}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="ទ្រឹស្តីបទស៊ីនុស"><span id=".E1.9E.91.E1.9F.92.E1.9E.9A.E1.9E.B9.E1.9E.9F.E1.9F.92.E1.9E.8F.E1.9E.B8.E1.9E.94.E1.9E.91.E2.80.8B.E1.9E.9F.E1.9F.8A.E1.9E.B8.E1.9E.93.E1.9E.BB.E1.9E.9F"></span><a href="/w/index.php?title=%E1%9E%91%E1%9F%92%E1%9E%9A%E1%9E%B9%E1%9E%9F%E1%9F%92%E1%9E%8F%E1%9E%B8%E1%9E%94%E1%9E%91%E2%80%8B%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&redlink=1" class="new" title="ទ្រឹស្តីបទស៊ីនុស (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">ទ្រឹស្តីបទស៊ីនុស</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F&action=edit&section=10" title="កែប្រែផ្នែក៖ ទ្រឹស្តីបទស៊ីនុស"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ទ្រឹស្តីបទស៊ីនុសចំពោះគ្រប់<a href="/wiki/%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E" title="ត្រីកោណ">ត្រីកោណ</a> ABC ដែលមានរង្វាស់ a, b, c និង <a href="/wiki/%E1%9E%98%E1%9E%BB%E1%9F%86" title="មុំ">មុំ</a>ឈមនឹងជ្រុងនិមួយៗរៀងគ្នា A, B, និង C សំដែងដោយ </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sin A}{a}}={\frac {\sin B}{b}}={\frac {\sin C}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>A</mi> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>B</mi> </mrow> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>C</mi> </mrow> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin A}{a}}={\frac {\sin B}{b}}={\frac {\sin C}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1e8929b4f629e8a791de1dedacddd8f7b6c9a7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.707ex; height:5.509ex;" alt="{\displaystyle {\frac {\sin A}{a}}={\frac {\sin B}{b}}={\frac {\sin C}{c}}}"></span></dd></dl> <p>បើ R ជា<a href="/wiki/%E1%9E%80%E1%9E%B6%E1%9F%86" title="កាំ">កាំ</a>នៃរង្វង់ចារឹកក្រៅត្រីកោណ ABC នោះទ្រឹស្តីបទសំដែងដោយ៖ </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a}{\sin A}}={\frac {b}{\sin B}}={\frac {c}{\sin C}}=2R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{\sin A}}={\frac {b}{\sin B}}={\frac {c}{\sin C}}=2R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d80986c9d20c3eb3943d11776d454f6462b9b1ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:29.732ex; height:5.509ex;" alt="{\displaystyle {\frac {a}{\sin A}}={\frac {b}{\sin B}}={\frac {c}{\sin C}}=2R}"></span></dd></dl> <p><br /> ចំពោះសេចក្តីលំអិតបន្ថែម សូមមើល<a href="/wiki/%E1%9E%91%E1%9F%92%E1%9E%9A%E1%9E%B9%E1%9E%9F%E1%9F%92%E1%9E%8F%E1%9E%B8%E1%9E%94%E1%9E%91%E1%9E%9F%E1%9F%8A%E1%9E%B8%E1%9E%93%E1%9E%BB%E1%9E%9F" title="ទ្រឹស្តីបទស៊ីនុស">ទ្រឹស្តីបទស៊ីនុស</a>។ </p> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐6df7948d6c‐rkmrm Cached time: 20241127172536 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.096 seconds Real time usage: 0.388 seconds Preprocessor visited node count: 633/1000000 Post‐expand include size: 475/2097152 bytes Template argument size: 170/2097152 bytes Highest expansion depth: 6/100 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