6.2 Trigonometric Functions: Unit Circle Approach/19: Difference between revisions
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\begin{align} | \begin{align} | ||
\sin{(t)} &= -\frac{1}{3} & \csc{(t)} &= -\frac{ | \sin{(t)} &= -\frac{1}{3} & \csc{(t)} &= -\frac{1}{-\frac{1}{3}} = \frac{1}{1}\cdot-\frac{3}{1} = -3\\[2ex] | ||
\cos{(t)} &= \frac{2\sqrt{2}}{3} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | \cos{(t)} &= \frac{2\sqrt{2}}{3} & \sec{(t)} &= \frac{1}{\frac{2\sqrt{2}}{3}} = \frac{1}{1}\cdot\frac{3}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}}{4}\\[2ex] | ||
\tan{(t)} &= \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}} = -\frac{1}{3}\cdot\frac{3}{2\sqrt{2}} = \frac{1}{2\sqrt{2}}\cdot\frac{ | \tan{(t)} &= \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}} = -\frac{1}{3}\cdot\frac{3}{2\sqrt{2}} = \frac{1}{2\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{4} & \cot{(t)} &= \frac{\frac{2\sqrt{2}}{3}}{-\frac{1}{3}} = \frac{2\sqrt{2}}{3}\cdot-\frac{3}{1} = -2\sqrt{2} \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 17:02, 30 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&=-{\frac {1}{3}}&\csc {(t)}&=-{\frac {1}{-{\frac {1}{3}}}}={\frac {1}{1}}\cdot -{\frac {3}{1}}=-3\\[2ex]\cos {(t)}&={\frac {2{\sqrt {2}}}{3}}&\sec {(t)}&={\frac {1}{\frac {2{\sqrt {2}}}{3}}}={\frac {1}{1}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {3}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {3{\sqrt {2}}}{4}}\\[2ex]\tan {(t)}&={\frac {-{\frac {1}{3}}}{\frac {2{\sqrt {2}}}{3}}}=-{\frac {1}{3}}\cdot {\frac {3}{2{\sqrt {2}}}}={\frac {1}{2{\sqrt {2}}}}\cdot {\frac {\sqrt {2}}{\sqrt {2}}}={\frac {\sqrt {2}}{4}}&\cot {(t)}&={\frac {\frac {2{\sqrt {2}}}{3}}{-{\frac {1}{3}}}}={\frac {2{\sqrt {2}}}{3}}\cdot -{\frac {3}{1}}=-2{\sqrt {2}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/bf26a2d4da636911311c755b4987e1f040758832)