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The sketch below shows the curves

\begin{aligned} y & = 2^{\sin x} \\ y & = 3^{\cos x} \end{aligned}

Two curves and six points

Find the coordinates of the labeled points, giving your answers to $3$ significant figures where appropriate.

At $A$ and $B$ , $x = 0$ .

At $C$ and $D$ , we must solve

2^{\sin (x)} = 3^{\cos (x)}

To find $E$ , we need to make $2^{\sin (x)}$ as large as possible. What values can $\sin (x)$ take?