θ → x = − 3 , y = 4 , r = 5 {\displaystyle \theta \rightarrow x=-3,\,y=4,\,r=5}
− 3 2 + 4 2 = 5 2 {\displaystyle -3^{2}+4^{2}=5^{2}}
9 + 16 = 25 {\displaystyle 9+16=25} 25 = 5 = r {\displaystyle {\sqrt {25}}=5=r} sin ( θ ) = 4 5 csc ( θ ) = 5 4 cos ( θ ) = − 3 5 sec ( θ ) = 5 − 3 tan ( θ ) = 4 − 3 cot ( θ ) = − 3 4 {\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {4}{5}}&\csc {(\theta )}&={\frac {5}{4}}\\[2ex]\cos {(\theta )}&={\frac {-3}{5}}&\sec {(\theta )}&={\frac {5}{-3}}\\[2ex]\tan {(\theta )}&={\frac {4}{-3}}&\cot {(\theta )}&={\frac {-3}{4}}\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}\sin {(\theta )}&={\frac {4}{5}}&\csc {(\theta )}&={\frac {5}{4}}\\[2ex]\cos {(\theta )}&={\frac {-3}{5}}&\sec {(\theta )}&={\frac {5}{-3}}\\[2ex]\tan {(\theta )}&={\frac {4}{-3}}&\cot {(\theta )}&={\frac {-3}{4}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/149146e08e4b0b08154c485ec21a7d3dd1ccbd42)