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