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