Answer
$\sin\theta=\frac{y}{r}=\frac{-1}{\sqrt {2}}=\frac{-\sqrt {2}}{2}$
$\cos\theta=\frac{x}{r}=\frac{1}{\sqrt {2}}=\frac{\sqrt {2}}{2}$
$\tan\theta=\frac{y}{x}=\frac{-1}{1}=-1$
$\csc\theta=\frac{1}{\sin\theta}=\frac{\sqrt {2}}{-1}=-\sqrt 2$
$\sec\theta=\frac{1}{\cos\theta}=\frac{\sqrt {2}}{1}=\sqrt 2$
$\cot\theta=\frac{1}{\tan\theta}=\frac{1}{-1}=-1$
Work Step by Step
$x=1$
$y=-1$
$r=\sqrt {(1)^{2}+(-1)^{2}}=\sqrt {1+1}=\sqrt {2}$
