## Trigonometry (11th Edition) Clone

To produce voltage $E=0$, it takes at least 2 seconds.
$$E=20\sin(\frac{\pi t}{4}-\frac{\pi}{2})$$ 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.