For the curve $x=3\cos \theta , y=3\sin \theta ,$$0\le \theta \le \pi$, the tangent is parallel to the x-axis, where $\theta =$

Solution:

For the tangent to be parallel to x-axis, we must
have

$\frac{dy}{dx}=0\Rightarrow \frac{{\displaystyle \frac{dy}{d\theta }}}{{\displaystyle \frac{dx}{d\theta }}}=0\Rightarrow \frac{3\cos \theta }{-3\sin \theta }=0\Rightarrow \cot \theta =0\Rightarrow \theta =\frac{\pi }{2}$