Answer
$\sqrt {1-u^2}$
Work Step by Step
Step 1. Letting $cos^{-1}u=t$, we have $cos(t)=u$
Step 2. Form a right triangle with sides $x=u,r=1,y=\sqrt {1-u^2}$ and angle $|t|$ facing $y$.
Step 3. We have $sin(cos^{-1}u)=sin(t)=\frac{y}{r}=\sqrt {1-u^2}$