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| <math> 200 \Rightarrow (\frac{7/pi}{6}</math><br><br> | | <math> 210 \Rightarrow (\frac{7\pi}{6}) \Rightarrow (\frac{-\sqrt{3}}{2},\frac{-1}{2})</math><br><br> |
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| <math> | | <math> |
| \begin{align} | | \begin{align} |
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| \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] | | \sin{\left(\frac{7\pi}{6}\right)} &= \frac{-1}{2} & \csc{\left(\frac{7\pi}{6}\right)} &= \frac{{1}} \frac{-1}{2} \cdot{2} = \frac{2}{-1} = -2 \\[2ex] |
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| \cos{\left(\frac{2\pi}{3}\right)} &= -\frac{1}{2} & \sec{\left(\frac{2\pi}{3}\right)} &= \frac{1}{-\frac{1}{2}} \cdot{2} = -\frac{2}{1} = -2 \\[2ex] | | \cos{\left(\frac{7\pi}{6}\right)} &= \frac{-\sqrt{3}}{2} & \sec{\left(\frac{7\pi}{6}\right)} &= \frac{1}{\frac{-\sqrt{3}}{2}} \cdot{2} = \frac{2}{-\sqrt{3}} \cdot{-\sqrt{3}} = \frac{2-\sqrt{3}}{3} \\[2ex] |
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| \tan{\left(\frac{2\pi}{3}\right)} &= \frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}} \cdot{2} = -\frac{\sqrt{3}}{1} = -\sqrt{3} | | \tan{\left(\frac{7\pi}{6}\right)} &= \frac{\frac{-\sqrt{3}}{2}}{\frac{-1}{2}} \cdot{2} = -\frac{\sqrt{3}}{1} = -\sqrt{3} |
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| & \cot{\left(\frac{2\pi}{3}\right)} &= -\frac{\sqrt{3}}{1}= -\sqrt{3} \\[2ex] | | & \cot{\left(\frac{7\pi}{6}\right)} &= \frac{\frac{-\sqrt{3}}{2}}{\frac{-1}{2}} \cdot{2} = -\frac{\sqrt{3}}{1} \\[2ex] |
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| \end{align} | | \end{align} |
| </math> | | </math> |
Latest revision as of 21:30, 1 September 2022
![{\displaystyle {\begin{aligned}\sin {\left({\frac {7\pi }{6}}\right)}&={\frac {-1}{2}}&\csc {\left({\frac {7\pi }{6}}\right)}&={\frac {1}{\frac {-1}{2}}}\cdot {2}={\frac {2}{-1}}=-2\\[2ex]\cos {\left({\frac {7\pi }{6}}\right)}&={\frac {-{\sqrt {3}}}{2}}&\sec {\left({\frac {7\pi }{6}}\right)}&={\frac {1}{\frac {-{\sqrt {3}}}{2}}}\cdot {2}={\frac {2}{-{\sqrt {3}}}}\cdot {-{\sqrt {3}}}={\frac {2-{\sqrt {3}}}{3}}\\[2ex]\tan {\left({\frac {7\pi }{6}}\right)}&={\frac {\frac {-{\sqrt {3}}}{2}}{\frac {-1}{2}}}\cdot {2}=-{\frac {\sqrt {3}}{1}}=-{\sqrt {3}}&\cot {\left({\frac {7\pi }{6}}\right)}&={\frac {\frac {-{\sqrt {3}}}{2}}{\frac {-1}{2}}}\cdot {2}=-{\frac {\sqrt {3}}{1}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c7cd2aba486e8ff53495153d611b852e860455d8)