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