6.2 Trigonometric Functions: Unit Circle Approach/78

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

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

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

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

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \sin{(\theta)} &= \frac{-12}{13} & \csc{(\theta)} &= \frac{2}{1}=2\\[2ex] \tan{(\theta)} &= \frac{\frac{1}{2}} & \cot{(\theta)} &= -\frac{\sqrt{3}}{1}= -\sqrt{3} \\[2ex] \end{align} }