Answer
$\sin\theta=\frac{-3}{5}$
Work Step by Step
1.We get this information from the sine value
$x=4$
$r=5$
2. We can use x and r to find y (we need to remember that sign of y depends on quadrant, since it ends in quadrant IV, it must be negative)
$r=\sqrt {y^{2}+x^{2}}$
$y=-\sqrt {r^{2}-x^{2}}=-\sqrt {5^{2}-4^{2}}=-\sqrt {25-16}=-\sqrt {9}=-3$
4. Then insert values,
$\sin\theta=\frac{-3}{5}$
