Answer
$-\frac{4}{5}$
Work Step by Step
Recall the identity $\sin^{2}\theta+\cos^{2}\theta=1$
$\implies (\frac{3}{5})^{2}+\cos^{2}\theta=1$
$\implies \cos^{2}\theta=1-\frac{9}{25}=\frac{16}{25}$
$\implies \cos\theta=\pm\frac{4}{5}$
$\cos\theta$ is negative in the second quadrant.
$\implies\cos\theta=-\frac{4}{5}$
