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