6.2 Trigonometric Functions: Unit Circle Approach/48: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 4: | Line 4: | ||
\begin{align} | \begin{align} | ||
\sin{\left(\frac{5\pi}{6}\right)} &= \frac{1}{2} & \csc{( | \sin{\left(\frac{5\pi}{6}\right)} &= \frac{1}{2} & \csc{\left(\frac{5\pi}{6}\right)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | ||
\cos{\left(\frac{5\pi}{6}\right)} &= \frac{-\sqrt{3}}{2} & \sec{( | |||
\tan{\left(\frac{5\pi}{6}\right)} &= \frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}} = -\frac{\sqrt{3}}{2}\cdot\frac{2}{1} = -\sqrt{3} & \cot{( | \cos{\left(\frac{5\pi}{6}\right)} &= \frac{-\sqrt{3}}{2} & \sec{\left(\frac{5\pi}{6}\right)} &= \frac{2}{1} = 2\\[2ex] | ||
\tan{\left(\frac{5\pi}{6}\right)} &= \frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}} = -\frac{\sqrt{3}}{2}\cdot\frac{2}{1} = -\sqrt{3} & \cot{\left(\frac{5\pi}{6}\right)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 22:26, 25 August 2022
![{\displaystyle {\begin{aligned}\sin {\left({\frac {5\pi }{6}}\right)}&={\frac {1}{2}}&\csc {\left({\frac {5\pi }{6}}\right)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {\left({\frac {5\pi }{6}}\right)}&={\frac {-{\sqrt {3}}}{2}}&\sec {\left({\frac {5\pi }{6}}\right)}&={\frac {2}{1}}=2\\[2ex]\tan {\left({\frac {5\pi }{6}}\right)}&={\frac {-{\frac {\sqrt {3}}{2}}}{\frac {1}{2}}}=-{\frac {\sqrt {3}}{2}}\cdot {\frac {2}{1}}=-{\sqrt {3}}&\cot {\left({\frac {5\pi }{6}}\right)}&=-{\frac {1}{\sqrt {3}}}=-{\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/474998634a63c470142fe8b3f7f10806a52ebe94)