Answer
$(a)$
$\sin \theta =\frac{y}{r}$
$\cos \theta =\frac{x}{r}$
$\tan \theta =\frac{y}{x}$
$\csc \theta =\frac{r}{y}$
$\sec \theta =\frac{r}{x}$
$\cot \theta =\frac{x}{y}$
$(b)$
$\sin \theta =\frac{4}{5}$
$\cos \theta =-\frac{3}{5}$
$\tan \theta =-\frac{4}{3}$
Work Step by Step
$(a)$
$\sin \theta =\frac{y}{r}$
$\cos \theta =\frac{x}{r}$
$\tan \theta =\frac{y}{x}$
$\csc \theta =\frac{r}{y}$
$\sec \theta =\frac{r}{x}$
$\cot \theta =\frac{x}{y}$
$(b)$
We have the following values :
$x=-3$
$y=4$
$r=\sqrt{(-3)^2+4^2}=\sqrt{25}=5$
Using the expressions in $(a)$ we can write :
$\sin \theta =\frac{4}{5}$
$\cos \theta =-\frac{3}{5}$
$\tan \theta =-\frac{4}{3}$
