6.2 Trigonometric Functions: Unit Circle Approach/78: Difference between revisions

Revision as of 17:00, 26 August 2022

$\theta \rightarrow (5,-12)$

$\theta \rightarrow x=5,\,y=-12,\,r=\,?$

${\begin{aligned}(5)^{2}+(-12)^{2}&=r^{2}\\25+144&=r^{2}\\169&=r^{2}\\{\sqrt {169}}&={\sqrt {r^{2}}}\\13&=r\\\end{aligned}}$

$\theta \rightarrow x=5,\,y=-12,\,r=13$

${\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {2}{1}}=2\\[2ex]\end{aligned}}$

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 \sin{(\theta)} &= \frac{-12}{13} & \csc{(\theta)} &= \frac{2}{1}=2\\[2ex]
-\cos{(\theta)} &= \frac{-\sqrt{3}}{2} & \sec{(\theta)} &= \frac{{2}}{-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\\[2ex]
-\tan{(\theta)} &= \frac{\frac{1}{2}} & \cot{(\theta)} &= -\frac{\sqrt{3}}{1}= -\sqrt{3} \\[2ex]
 \end{align}
 </math>