Answer
$\sin\theta$ = 0
$\cos\theta$ = -1
$\tan\theta$ = 0
$\cot\theta$ = Undefined
$\sec\theta$ = -1
$\csc\theta$ = Undefined
Work Step by Step
Given, point (-3, 0) is on the terminal side of $\theta$, we may apply Definition I to find all six trigonometric functions-
We got $ x = -3, y = 0$
Therefore r= $\sqrt (x^{2} + y^{2})$
= $\sqrt ((-3)^{2} + (0)^{2})$
= $\sqrt (9 + 0)$
= $\sqrt (9)$ = 3
i.e. $ x = -3, y = 0,$ and $ r= 3$
Applying Definition I-
$\sin\theta$ =$ \frac{y}{r}$ = $ \frac{0}{3}$ = 0
$\cos\theta$ =$ \frac{x}{r}$ =$ \frac{-3}{3}$ = -1
$\tan\theta$ =$ \frac{y}{x}$ =$ \frac{0}{-3}$ = 0
$\cot\theta$ =$ \frac{x}{y}$ =$ \frac{-3}{0}$ = Undefined
$\sec\theta$ =$ \frac{r}{x}$ =$ \frac{3}{-3}$ = -1
$\csc\theta$ =$ \frac{r}{y}$ =$ \frac{3}{0}$ = Undefined
