Answer
$\cos\theta$ = - $\frac{3}{5}$
Work Step by Step
We know from first Pythagorean identity that-
$\cos\theta$ = ± $\sqrt (1-\sin^{2}\theta)$
As $\theta$ terminates in Q III, Therefore $\cos\theta$ will be negative-
$\cos\theta$ = - $\sqrt (1-\sin^{2}\theta)$
substitute the given value of $\sin\theta$-
$\cos\theta$ = - $\sqrt (1-(\frac{-4}{5})^{2})$
$\cos\theta$ = - $\sqrt (1-\frac{16}{25})$
$\cos\theta$ = - $\sqrt (\frac{25 - 16}{25})$ = $\sqrt (\frac{9}{25})$
$\cos\theta$ = - $\frac{3}{5}$
