Answer
1. $sin(\theta)= -\frac{12}{13}$.
2. $cos(\theta)= \frac{5}{13}$.
3. $tan(\theta)= -\frac{12}{5}$.
4. $cot(\theta)= -\frac{5}{12}$.
5. $sec(\theta)= \frac{13}{5}$.
6. $csc(\theta)= -\frac{13}{12}$.
Work Step by Step
Given point $(5,-12)$, we have $x=5, y=-12, r=\sqrt {(5)^2+(-12)^2}=13$, we have:
1. $sin(\theta)= \frac{y}{r}= -\frac{12}{13}$.
2. $cos(\theta)= \frac{x}{r}= \frac{5}{13}$.
3. $tan(\theta)= \frac{y}{x}=-\frac{12}{5}$.
4. $cot(\theta)=\frac{1}{tan(\theta)}=-\frac{5}{12}$.
5. $sec(\theta)=\frac{1}{cos(\theta)}=\frac{13}{5}$.
6. $csc(\theta)=\frac{1}{sin(\theta)}=-\frac{13}{12}$.
