6.2 Trigonometric Functions: Unit Circle Approach/63: Difference between revisions
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\sin{\left(\frac{-14\pi}{3}\right)} &= -\frac{\sqrt{3}}{2} & \csc{\left(\frac{-14\pi}{3}\right)} &= \frac{1}{\frac{\sqrt{3}}{2}} | \sin{\left(\frac{-14\pi}{3}\right)} &= -\frac{\sqrt{3}}{2} & \csc{\left(\frac{-14\pi}{3}\right)} &= \frac{1}{\frac{\sqrt{3}}{2}} | ||
\cos{\left(\frac{-14\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{-14\pi}{3}\right)} &= \frac{{2}}{-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\\[2ex] | \cos{\left(\frac{-14\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{-14\pi}{3}\right)} &= \frac{{2}}{-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\\[2ex] | ||
Revision as of 16:13, 29 August 2022
![{\displaystyle {\begin{aligned}\sin {\left({\frac {-14\pi }{3}}\right)}&=-{\frac {\sqrt {3}}{2}}&\csc {\left({\frac {-14\pi }{3}}\right)}&={\frac {1}{\frac {\sqrt {3}}{2}}}\cos {\left({\frac {-14\pi }{3}}\right)}&=-{\frac {1}{2}}&\sec {\left({\frac {-14\pi }{3}}\right)}&={\frac {2}{-{\sqrt {3}}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}=-{\frac {2{\sqrt {3}}}{3}}\\[2ex]\tan {\left({\frac {-14\pi }{3}}\right)}&={\frac {{\cancel {-}}{\frac {\sqrt {3}}{2}}}{{\cancel {-}}{\frac {1}{2}}}}={\frac {\sqrt {3}}{\cancel {2}}}\cdot {\cancel {2}}={\sqrt {3}}&\cot {\left({\frac {-14\pi }{3}}\right)}&=-{\frac {\sqrt {3}}{1}}=-{\sqrt {3}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/0d563dbff0e450a1491e65d0d14ff41c041e33e6)