Answer
Express the formula of $E$ in terms of $\cos\frac{\pi t}{4}$:
$$E=-20\cos\frac{\pi t}{4}$$
Work Step by Step
$$E=20\sin\Big(\frac{\pi t}{4}-\frac{\pi}{2}\Big)$$
For $\sin\Big(\frac{\pi t}{4}-\frac{\pi}{2}\Big)$, the identity of the difference of sines can be applied.
$$\sin(A-B)=\sin A\cos B-\cos A\sin B$$
which means $$\sin\Big(\frac{\pi t}{4}-\frac{\pi}{2}\Big)=\sin\frac{\pi t}{4}\cos\frac{\pi}{2}-\cos\frac{\pi t}{4}\sin\frac{\pi}{2}$$
$$\sin\Big(\frac{\pi t}{4}-\frac{\pi}{2}\Big)=\sin\frac{\pi t}{4}\times0-\cos\frac{\pi t}{4}\times1$$
$$\sin\Big(\frac{\pi t}{4}-\frac{\pi}{2}\Big)=-\cos\frac{\pi t}{4}$$
Therefore, $E$ can be written as
$$E=20\times\Big(-\cos\frac{\pi t}{4}\Big)$$
$$E=-20\cos\frac{\pi t}{4}$$
