6.2 Trigonometric Functions: Unit Circle Approach/17: Difference between revisions
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\sin{(t)} &= \frac{\sqrt{2}}{2} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | \sin{(t)} &= \frac{\sqrt{2}}{2} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | ||
\cos{(t)} &= -\frac{\sqrt{2}}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | \cos{(t)} &= -\frac{\sqrt{2}}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | ||
\tan{(t)} &= \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \cdot{2} & \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{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \cdot{2} = -\frac{\sqrt{2}} \sqrt{2} & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 17:52, 30 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&={\frac {\sqrt {2}}{2}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {(t)}&=-{\frac {\sqrt {2}}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {(t)}&={\frac {\frac {\sqrt {2}}{2}}{-{\frac {\sqrt {2}}{2}}}}\cdot {2}=-{\frac {\sqrt {2}}{\sqrt {2}}}&\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/0201f21a4e69324e29d311bf6f124ad8e2b07f3e)