Answer
To produce voltage $E=0$, it takes at least 2 seconds.
Work Step by Step
$$E=20\sin(\frac{\pi t}{4}-\frac{\pi}{2})$$
Since $t$ is time in seconds, the range of $t$ is $[0,\pi)$
For $E=0$, we get the equation
$$20\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$
$$\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$$
For $\frac{\pi t}{4}-\frac{\pi}{2}=0$, we would get $\sin(\frac{\pi t}{4}-\frac{\pi}{2})=0$. Also we would get the least positive $t$ through this.
$$\frac{\pi t}{4}-\frac{\pi}{2}=0$$
$$\frac{\pi t}{4}=\frac{\pi}{2}$$
$$t=\frac{\pi}{2}\times\frac{4}{\pi}$$
$$t=2(seconds)$$
So to produce voltage $E=0$, it takes at least 2 seconds.
