6.2 Trigonometric Functions: Unit Circle Approach/17: Difference between revisions
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\begin{align} | \begin{align} | ||
\sin{(t)} &= \frac{\sqrt{2}}{2} & \csc{(t)} &= | \sin{(t)} &= \frac{\sqrt{2}}{2} & \csc{(t)} &= \frac{1}{\frac{\sqrt{2}}{2}} \cdot{2} = \frac{2}{\sqrt{2}} \cdot{\sqrt{2}} \\[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} = -\frac{\sqrt{2}} \sqrt{2} = -1 & \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} = -1 & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | ||
Revision as of 18:05, 30 August 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}}\\[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}}}=-1&\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/5a0654d49accc5348eeb2cd1c30a151efeecf7ad)