Answer
$\cos\theta$ = $\sqrt {1-\sin^{2}\theta}$
($\cos\theta\gt0$ and $\sin\theta\lt0$ as $\theta$ lies in quadrant IV)
Work Step by Step
We are supposed to write $\cos\theta$ in terms of $\sin\theta$ while $\theta$ lies in Quadrant IV.
From Pythagorean identity-
$\cos\theta$ may be written as $\sqrt {1-\sin^{2}\theta}$
Therefore-
$\cos\theta$ = $\sqrt {1-\sin^{2}\theta}$
($\cos\theta\gt0$ and $\sin\theta\lt0$ as $\theta$ lies in quadrant IV)
