6.2 Trigonometric Functions: Unit Circle Approach/13: Difference between revisions
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\begin{align} | \begin{align} | ||
\sin{(t)} &= \frac{1}{2} & \csc{(t)} &= | \sin{(t)} &= \frac{1}{2} & \csc{(t)} &= \frac{1}{\frac{1}{2}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | ||
\cos{(t)} &= \frac{\sqrt{3}}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | \cos{(t)} &= \frac{\sqrt{3}}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | ||
\tan{(t)} &= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\cancel{2}}\cdot\frac{\cancel{2}}{\sqrt{3}} = \frac{1}{\cancel{\sqrt{3}}} \cdot \frac{\cancel{\sqrt{3}}}{\sqrt{3}}=\frac{\sqrt{3}}{3} & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | \tan{(t)} &= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\cancel{2}}\cdot\frac{\cancel{2}}{\sqrt{3}} = \frac{1}{\cancel{\sqrt{3}}} \cdot \frac{\cancel{\sqrt{3}}}{\sqrt{3}}=\frac{\sqrt{3}}{3} & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | ||
Revision as of 17:01, 26 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&={\frac {1}{2}}&\csc {(t)}&={\frac {1}{\frac {1}{2}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {(t)}&={\frac {\sqrt {3}}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {(t)}&={\frac {\frac {1}{2}}{\frac {\sqrt {3}}{2}}}={\frac {1}{\cancel {2}}}\cdot {\frac {\cancel {2}}{\sqrt {3}}}={\frac {1}{\cancel {\sqrt {3}}}}\cdot {\frac {\cancel {\sqrt {3}}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}&\cot {(t)}&=-{\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/8202c8d5c3ba5972d9db0d8dc33b5a064f5fcf62)