Answer
$\frac{4}{5}$
Work Step by Step
Step 1. Letting $cot^{-1}(\frac{3}{4})=t$, we have $cot(t)=\frac{3}{4}$ with $0\lt t \lt \frac{\pi}{2}$
Step 2. Form a right triangle of $x=3, y=4, r=5$ with angle $t$ facing $y$.
Step 3. We have $sin(cot^{-1}(\frac{3}{4}))=sin(t)=\frac{4}{5}$
