Answer
$$t=\frac{1}{4}$$
Work Step by Step
$$V=\cos2\pi t$$
where $t\in[0,\frac{1}{2}]$
As $V=0$, we would have the equation: $$\cos2\pi t=0$$
We would take the interval $[0,2\pi)$ here.
Over the interval $[0,2\pi)$, there are 2 values of $2\pi t$ where $\cos2\pi t=0$, which are $\frac{\pi}{2}$ and $\frac{3\pi}{2}$.
That means $$2\pi t=\frac{\pi}{2}\hspace{1cm}\text{or}\hspace{1cm}2\pi t=\frac{3\pi}{2}$$
$$t=\frac{\pi}{2\times2\pi}\hspace{1cm}\text{or}\hspace{1cm}t=\frac{3\pi}{2\times2\pi}$$
$$t=\frac{1}{4}\hspace{1cm}\text{or}\hspace{1cm}t=\frac{3}{4}$$
$t=\frac{3}{4}$ lies out of the defined interval for $t$: $t\in[0,\frac{1}{2}]$, so we need to eliminate $t=\frac{3}{4}$
That means $t=\frac{1}{4}$ is the result of this question.
