6.2 Trigonometric Functions: Unit Circle Approach/47: Difference between revisions
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\begin{align} | \begin{align} | ||
\sin{\left(\frac{2\pi}{3}\right)} &= \frac{\sqrt{3}}{2} & \csc{\left(\frac{2\pi}{3}\right)} &= \frac{{1}} \frac{\sqrt{3}}{2} \cdot{2} = \frac{2}{\sqrt{3}} \cdot{\sqrt{3}} \\[2ex] | \sin{\left(\frac{2\pi}{3}\right)} &= \frac{\sqrt{3}}{2} & \csc{\left(\frac{2\pi}{3}\right)} &= \frac{{1}} \frac{\sqrt{3}}{2} \cdot{2} = \frac{2}{\sqrt{3}} \cdot{\sqrt{3}} = \frac{2\sqrt{3}}{3} \\[2ex] | ||
\cos{\left(\frac{2\pi}{3}\right)} &= -\frac{1}{2} & \sec{\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{2\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{5\pi}{6}\right)} &= \frac{{2}}{-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\\[2ex] | ||
Revision as of 16:17, 1 September 2022
![{\displaystyle {\begin{aligned}\sin {\left({\frac {2\pi }{3}}\right)}&={\frac {\sqrt {3}}{2}}&\csc {\left({\frac {2\pi }{3}}\right)}&={\frac {1}{\frac {\sqrt {3}}{2}}}\cdot {2}={\frac {2}{\sqrt {3}}}\cdot {\sqrt {3}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {\left({\frac {2\pi }{3}}\right)}&=-{\frac {1}{2}}&\sec {\left({\frac {5\pi }{6}}\right)}&={\frac {2}{-{\sqrt {3}}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}=-{\frac {2{\sqrt {3}}}{3}}\\[2ex]\tan {\left({\frac {2\pi }{3}}\right)}&={\frac {\frac {\sqrt {3}}{2}}{-{\frac {1}{2}}}}\cdot {2}=-{\frac {\sqrt {3}}{1}}=-{\sqrt {3}}&\cot {\left({\frac {5\pi }{6}}\right)}&=-{\frac {\sqrt {3}}{1}}=-{\sqrt {3}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/b8149d37d8d426a4838fb0b2f6399a87143ebb27)