6.2 Trigonometric Functions: Unit Circle Approach/79

$\theta \rightarrow x=2,\,y=-3,\,r={\sqrt {13}}$

$-3^{2}+4^{2}=5^{2}$

$9+16=25$

${\sqrt {25}}=5=r$

${\begin{aligned}\sin {(\theta )}&=-{\frac {3{\sqrt {13}}}{13}}&\csc {(\theta )}&=-{\frac {\sqrt {13}}{3}}\\[2ex]\cos {(\theta )}&={\frac {-3}{5}}&\sec {(\theta )}&={\frac {5}{-3}}\\[2ex]\tan {(\theta )}&={\frac {-3}{2}}&\cot {(\theta )}&={\frac {-2}{3}}\\[2ex]\end{aligned}}$