6.2 Trigonometric Functions: Unit Circle Approach/17: Difference between revisions
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(Created page with "<math>\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)</math> <math> \begin{align} \sin{(t)} &= -\frac{\sqrt{3}}{2} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] \cos{(t)} &= \frac{1}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] \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{\s...") |
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<math>\left(\frac{ | <math>\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)</math> | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
\sin{(t)} &= | \sin{(t)} &= \frac{\sqrt{2}}{2} & \csc{(t)} &= \frac{1}{\frac{\sqrt{2}}{2}} \cdot{2} = \frac{2}{\sqrt{2}} \cdot{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \\[2ex] | ||
\cos{(t)} &= \frac{ | \cos{(t)} &= -\frac{\sqrt{2}}{2} & \sec{(t)} &= \frac{1}{\frac{-\sqrt{2}}{2}} \cdot{2} = \frac{2}{-\sqrt{2}} \cdot{\sqrt{2}} = -\frac{2\sqrt{2}}{2} = -\sqrt{2} \\[2ex] | ||
\tan{(t)} &= \frac{ | \tan{(t)} &= \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \cdot{2} = -\frac{\sqrt{2}} \sqrt{2} = -1 & \cot{(t)} &= \frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \cdot{2} = -\frac{\sqrt{2}} \sqrt{2} = -1 \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 15:59, 1 September 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&={\frac {\sqrt {2}}{2}}&\csc {(t)}&={\frac {1}{\frac {\sqrt {2}}{2}}}\cdot {2}={\frac {2}{\sqrt {2}}}\cdot {\sqrt {2}}={\frac {2{\sqrt {2}}}{2}}={\sqrt {2}}\\[2ex]\cos {(t)}&=-{\frac {\sqrt {2}}{2}}&\sec {(t)}&={\frac {1}{\frac {-{\sqrt {2}}}{2}}}\cdot {2}={\frac {2}{-{\sqrt {2}}}}\cdot {\sqrt {2}}=-{\frac {2{\sqrt {2}}}{2}}=-{\sqrt {2}}\\[2ex]\tan {(t)}&={\frac {\frac {\sqrt {2}}{2}}{-{\frac {\sqrt {2}}{2}}}}\cdot {2}=-{\frac {\sqrt {2}}{\sqrt {2}}}=-1&\cot {(t)}&={\frac {-{\frac {\sqrt {2}}{2}}}{\frac {\sqrt {2}}{2}}}\cdot {2}=-{\frac {\sqrt {2}}{\sqrt {2}}}=-1\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/afd5792ff0c2342cfa54d9f09ea3431fa65ce0c8)