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 ) = 13 − 12 cos ( θ ) = 5 13 sec ( θ ) = 13 5 tan ( θ ) = − 12 5 cot ( θ ) = 5 − 12 {\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {13}{-12}}\\[2ex]\cos {(\theta )}&={\frac {5}{13}}&\sec {(\theta )}&={\frac {13}{5}}\\[2ex]\tan {(\theta )}&={\frac {-12}{5}}&\cot {(\theta )}&={\frac {5}{-12}}\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {13}{-12}}\\[2ex]\cos {(\theta )}&={\frac {5}{13}}&\sec {(\theta )}&={\frac {13}{5}}\\[2ex]\tan {(\theta )}&={\frac {-12}{5}}&\cot {(\theta )}&={\frac {5}{-12}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/b879455487c38600d902c07327ede3e69912a477)