Answer
$\theta = \frac{3\pi}{2}$
We can find the values of the six trigonometric functions:
$sin ~\theta = -1$
$cos ~\theta = 0$
$tan ~\theta~~$ is undefined
$csc ~\theta = -1$
$sec ~\theta~~$ is undefined
$cot ~\theta = 0$
Work Step by Step
$x = 0$
$y = -2$
$\theta = \frac{3\pi}{2}$
We can find the values of the six trigonometric functions:
$sin ~\theta = sin~\frac{3\pi}{2} = -1$
$cos ~\theta =cos~\frac{3\pi}{2} = 0$
$tan ~\theta = \frac{sin~\frac{3\pi}{2} }{cos~\frac{3\pi}{2}}~~$ which is undefined
$csc ~\theta = \frac{1}{sin~\frac{3\pi}{2}} = -1$
$sec ~\theta = \frac{1}{cos~\frac{3\pi}{2}}~~$ which is undefined
$cot ~\theta = \frac{cos~\frac{3\pi}{2} }{sin~\frac{3\pi}{2}} = 0$
