Answer
$\cos\theta$ = - $\frac{1}{2}$
Work Step by Step
We know from first Pythagorean identity that-
$\cos\theta$ = ± $\sqrt (1-\sin^{2}\theta)$
As $\theta$ terminates in Q I, Therefore $\cos\theta$ will be negative-
$\cos\theta$ = - $\sqrt (1-\sin^{2}\theta)$
substitute the given value of $\sin\theta$-
$\cos\theta$ = - $\sqrt (1-(\frac{\sqrt 3}{2})^{2})$
$\cos\theta$ = - $\sqrt (1-\frac{3}{4})$
$\cos\theta$ = - $\sqrt (\frac{4 - 3}{4})$ = $\sqrt (\frac{1}{4})$
$\cos\theta$ = - $\frac{1}{2}$
