Answer
$\sin\theta$ = -1
$\cos\theta$ = 0
$\tan\theta$ = Undefined
$\cot\theta$ = 0
$\sec\theta$ = Undefined
$\csc\theta$ = - 1
Work Step by Step
Given, point (0, -5) is on the terminal side of $\theta$, we may apply Definition I to find all six trigonometric functions-
We got $ x = 0, y = -5$
Therefore r= $\sqrt (x^{2} + y^{2})$
= $\sqrt ((0)^{2} + (-5)^{2})$
= $\sqrt (0 + 25)$
= $\sqrt (25)$ = 5
i.e. $ x = 0, y = -5,$ and $ r= 5$
Applying Definition I-
$\sin\theta$ =$ \frac{y}{r}$ = $ \frac{-5}{5}$ = -1
$\cos\theta$ =$ \frac{x}{r}$ =$ \frac{0}{5}$ = 0
$\tan\theta$ =$ \frac{y}{x}$ =$ \frac{-5}{0}$ = Undefined
$\cot\theta$ =$ \frac{x}{y}$ =$ \frac{0}{-5}$ = 0
$\sec\theta$ =$ \frac{r}{x}$ =$ \frac{5}{0}$ = Undefined
$\csc\theta$ =$ \frac{r}{y}$ =$ \frac{5}{-5}$ = - 1
