Source / pinned edition
Derivatives of Trigonometric Functions
Source of package openstax.calculus_derivatives · OpenStax Calculus, ch. 3 Derivatives, module m53578
- work
- urn:openstax:clir:calculus-derivatives#M53578
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- OpenStax Calculus, ch. 3 Derivatives, module m53578
- kind
- urn:openstax:clir:calculus-derivatives#treatise
m53578/index.cnxml at commit 8dbc2ce (main, 2026-07-15)
- edition
- urn:openstax:clir:calculus-derivatives#M53578_MAIN
- language
- en
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- official
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- PINNED_OFFICIAL_BYTES
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- adopted: 2026-07-15
Publications
| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://raw.githubusercontent.com/openstax/osbooks-calculus-bundle/8dbc2ce19e804924b2517b89ac72ee45be949d15/modules/m53578/index.cnxml | application/xml; charset=utf-8 | sha256:68d65321d8a387027ec0f236860f653000ea77100a7a59b057d0297a9a9c9c9f | 2026-09-12T00:00:00Z |
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module/m53578#fs-id1169739098813 · section · referenced by: 2
en · official · sha256:356216338116ba0327ab7f84cf12756a619a9ae7cb328ba2c52b3a419fd34291
<note id="fs-id1169739098813" class="theorem">
<title>The Derivatives of sin <emphasis effect="italics">x</emphasis> and cos <emphasis effect="italics">x</emphasis></title>
<para id="fs-id1169738998734">The derivative of the sine function is the cosine and the derivative of the cosine function is the negative sine.</para>
<equation id="fs-id1169738884040"><m:math><m:mrow><m:mfrac><m:mi>d</m:mi><m:mrow><m:mi>d</m:mi><m:mi>x</m:mi></m:mrow></m:mfrac><m:mrow><m:mo>(</m:mo><m:mrow><m:mtext>sin</m:mtext><m:mspace width="0.1em"/><m:mi>x</m:mi></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mtext>cos</m:mtext><m:mspace width="0.1em"/><m:mi>x</m:mi></m:mrow></m:math></equation>
<equation id="fs-id1169739096692"><m:math><m:mrow><m:mfrac><m:mi>d</m:mi><m:mrow><m:mi>d</m:mi><m:mi>x</m:mi></m:mrow></m:mfrac><m:mrow><m:mo>(</m:mo><m:mrow><m:mtext>cos</m:mtext><m:mspace width="0.1em"/><m:mi>x</m:mi></m:mrow><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mtext>−</m:mtext><m:mtext>sin</m:mtext><m:mspace width="0.1em"/><m:mi>x</m:mi></m:mrow></m:math></equation>
</note>Referencing norms: CosineJustifies, SineJustifies
The hash beside the text is the sha256 of its exact bytes. It is the check that the text shown matches the one pinned in the package: a divergence fails the oracle’s static analysis.