θ → ( 5 , − 12 ) {\displaystyle \theta \rightarrow (5,-12)}
θ → x = 5 , y = − 12 , r = ? {\displaystyle \theta \rightarrow x=5,\,y=-12,\,r=\,?}
( 5 ) 2 + ( − 12 ) 2 = r 2 25 + 144 = r 2 169 = r 2 169 = r 2 13 = r {\displaystyle {\begin{aligned}(5)^{2}+(-12)^{2}&=r^{2}\\25+144&=r^{2}\\169&=r^{2}\\{\sqrt {169}}&={\sqrt {r^{2}}}\\13&=r\\\end{aligned}}}
θ → x = 5 , y = − 12 , r = 13 {\displaystyle \theta \rightarrow x=5,\,y=-12,\,r=13}
sin ( θ ) = − 12 13 csc ( θ ) = 2 1 = 2 cos ( θ ) = − 3 2 sec ( θ ) = 3 tan ( θ ) = 2 3 cot ( θ ) = 3 {\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {2}{1}}=2\\[2ex]\cos {(\theta )}&={\frac {-{\sqrt {3}}}{2}}&\sec {(\theta )}&=3\\[2ex]\tan {(\theta )}&={\frac {2}{3}}&\cot {(\theta )}&=3\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {2}{1}}=2\\[2ex]\cos {(\theta )}&={\frac {-{\sqrt {3}}}{2}}&\sec {(\theta )}&=3\\[2ex]\tan {(\theta )}&={\frac {2}{3}}&\cot {(\theta )}&=3\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ab4ca4584864e17b3deff40baff5ca61e7d5d6ce)