Answer
+- $\frac{\sqrt 5}{3} $
Work Step by Step
Given-
$\cos \theta$ = - $\frac{2}{3}$, $\theta$ terminates in QIII
From first Pythagorean identity-
$\sin \theta$ = ± $\sqrt {1 - \cos^{2} \theta}$
As $\theta$ terminates in QIII, therefore
$\sin \theta$ = - $\sqrt {1 - \cos^{2} \theta}$
=+ - $\sqrt {1 - (- \frac{2}{3})^{2} }$
= +- $\sqrt {1 - \frac{4}{9} }$
= +- $\sqrt {\frac{9 - 4}{9} }$
= +- $\sqrt {\frac{5}{9} }$
= +- $\frac{\sqrt 5}{3} $
