Question

find the exact value of the sine of the angle at the point (4, -3).
$\frac{4}{5}$
$-\frac{3}{4}$
$-\frac{4}{3}$
$-\frac{3}{5}$

Explanation:

Step1: Calculate radius $r$

For point $(x,y)=(4,-3)$, use $r=\sqrt{x^2+y^2}$

$$ r=\sqrt{4^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5 $$

Step2: Compute sine of the angle

Use $\sin\theta=\frac{y}{r}$

$$ \sin\theta=\frac{-3}{5}=-\frac{3}{5} $$

Answer:

D. $-\frac{3}{5}$