Answer
\[\begin{align}
& \mathbf{a}\mathbf{.}\text{ }3 \\
& \mathbf{b}\mathbf{.}\text{ 0} \\
& \mathbf{c}\mathbf{.}\text{ }-\text{3} \\
\end{align}\]
Work Step by Step
\[\begin{align}
& \text{Let }g\left( x \right)=f\left( \sin x \right) \\
& g'\left( x \right)=\frac{d}{dx}\left[ f\left( \sin x \right) \right] \\
& \text{By the chain rule} \\
& g'\left( x \right)=f'\left( \sin x \right)\frac{d}{dx}\left[ \sin x \right] \\
& g'\left( x \right)=f'\left( \sin x \right)\left( \cos x \right) \\
& \\
& \mathbf{a}\mathbf{.}\text{ Calculate }g'\left( 0 \right) \\
& g'\left( 0 \right)=f'\left( \sin 0 \right)\left( \cos 0 \right) \\
& g'\left( 0 \right)=f'\left( \sin 0 \right)\left( 1 \right) \\
& g'\left( 0 \right)=f'\left( 0 \right) \\
& \text{Where }f'\left( 0 \right)=3,\text{ then} \\
& g'\left( 0 \right)=3 \\
& \\
& \mathbf{b}\mathbf{.}\text{ Calculate }g'\left( \frac{\pi }{2} \right) \\
& g'\left( \frac{\pi }{2} \right)=f'\left( \sin \frac{\pi }{2} \right)\left( \cos \frac{\pi }{2} \right) \\
& g'\left( \frac{\pi }{2} \right)=f'\left( 1 \right)\left( 0 \right) \\
& \text{Where }f'\left( 1 \right)=5,\text{ then} \\
& g'\left( \frac{\pi }{2} \right)=\left( 5 \right)\left( 0 \right) \\
& g'\left( \frac{\pi }{2} \right)=0 \\
& \\
& \mathbf{c}\mathbf{.}\text{ Calculate }g'\left( \pi \right) \\
& g'\left( \pi \right)=f'\left( \sin \pi \right)\left( \cos \pi \right) \\
& g'\left( \pi \right)=f'\left( 0 \right)\left( -1 \right) \\
& \text{Where }f'\left( 0 \right)=3,\text{ then} \\
& g'\left( \pi \right)=\left( 3 \right)\left( -1 \right) \\
& g'\left( \pi \right)=-3 \\
\end{align}\]
