The points on the curve y = sin x where the tangent lines are parallel to x - axis are given by

$$\begin{gathered} \mathrm{equation} \mathrm{of} \mathrm{given} \mathrm{curve} \mathrm{is} y=\sin x \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = 0 \\ \mathrm{Tangent} \mathrm{lines} \mathrm{are} \mathrm{parallel} \mathrm{to} \mathrm{x} - \mathrm{axis} \\ \Rightarrow \mathrm{slope} \mathrm{of} \mathrm{tangent}=0 \\ \Rightarrow \mathrm{cosx} = 0 \\ \therefore \mathrm{x}= \left(2\mathrm{n}+ 1\right)\frac{\mathrm{\pi }}{2} \mathrm{where} \mathrm{n}\in \mathrm{z} \end{gathered}$$