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| \begin{align} | | \begin{align} |
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| \sin{(t)} &= -\frac{\sqrt{3}}{2} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | | \sin{(t)} &= -\frac{1}{3} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] |
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| \cos{(t)} &= \frac{1}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | | \cos{(t)} &= \frac{2\sqrt{2}}{3} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] |
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| \tan{(t)} &= \frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}} = -\frac{\sqrt{3}}{2}\cdot\frac{2}{1} = -\sqrt{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}{3}}{\frac{2\sqrt{2}}{3}} = -\frac{1}{3}\cdot\frac{3}{2\sqrt{2}} = \frac{2\sqrt{2}}{4} & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] |
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| \end{align} | | \end{align} |
| </math> | | </math> |
Revision as of 17:11, 26 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&=-{\frac {1}{3}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {(t)}&={\frac {2{\sqrt {2}}}{3}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {(t)}&={\frac {-{\frac {1}{3}}}{\frac {2{\sqrt {2}}}{3}}}=-{\frac {1}{3}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {2{\sqrt {2}}}{4}}&\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/d66efb7bb87f4a6b45a4d0ac557ff50ae7e9b5b9)