Answer
$\cot\theta$ = $\frac{3}{2}$
Work Step by Step
Ratio identity for $\cot\theta$ is-
$\cot\theta$ = $\frac{\cos\theta}{\sin\theta}$
Substituting given values of $\sin\theta$ and $\cos\theta$-
$\cot\theta$ = $\frac{\frac{3\sqrt 13}{13}}{\frac{2\sqrt 13}{13}}$
= $\frac{3\sqrt 13\times 13}{2\sqrt 13\times13}$ = $\frac{3}{2}$
or $\cot\theta$ = $\frac{3}{2}$
