6.2 Trigonometric Functions: Unit Circle Approach/13: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 6: | Line 6: | ||
\sin{(t)} &= \frac{1}{2} & \csc{(t)} &= \frac{1}{\frac{1}{2}}=2\\[2ex] | \sin{(t)} &= \frac{1}{2} & \csc{(t)} &= \frac{1}{\frac{1}{2}}=2\\[2ex] | ||
\cos{(t)} &= \frac{\sqrt{3}}{2} & \sec{(t)} &= \frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}\\[2ex] | \cos{(t)} &= \frac{\sqrt{3}}{2} & \sec{(t)} &= \frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}\\[2ex] | ||
\tan{(t)} &= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\cancel{2}}\cdot\frac{\cancel{2}}{\sqrt{3}} = \frac{1}{\cancel{\sqrt{3}}} \cdot \frac{\cancel{\sqrt{3}}}{\sqrt{3}}=\frac{\sqrt{3}}{3} & \cot{(t)} &= \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} \\[2ex] | \tan{(t)} &= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\cancel{2}}\cdot\frac{\cancel{2}}{\sqrt{3}} = \frac{1}{\cancel{\sqrt{3}}} \cdot \frac{\cancel{\sqrt{3}}}{\sqrt{3}}=\frac{\sqrt{3}}{3} & \cot{(t)} &= \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{sqrt{3}}{2}/cdot 2 \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 17:11, 26 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&={\frac {1}{2}}&\csc {(t)}&={\frac {1}{\frac {1}{2}}}=2\\[2ex]\cos {(t)}&={\frac {\sqrt {3}}{2}}&\sec {(t)}&={\frac {1}{\frac {\sqrt {3}}{2}}}={\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\tan {(t)}&={\frac {\frac {1}{2}}{\frac {\sqrt {3}}{2}}}={\frac {1}{\cancel {2}}}\cdot {\frac {\cancel {2}}{\sqrt {3}}}={\frac {1}{\cancel {\sqrt {3}}}}\cdot {\frac {\cancel {\sqrt {3}}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}&\cot {(t)}&={\frac {\frac {\sqrt {3}}{2}}{\frac {1}{2}}}={\frac {sqrt{3}}{2}}/cdot2\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/379074e82fb73b9716e6653d11ae9ec89850e2c1)