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