## Trigonometry (11th Edition) Clone

$\frac{1}{8}$ seconds
To find the time when the weight first reaches maximum hieght, we need to substitute the maximum hieght (amplitude) into the formula and then solving for $t$: $s(t)=-4\cos 8\pi t$ $4=-4\cos 8\pi t$ $\frac{4}{-4}=\cos 8\pi t$ $-1=\cos 8\pi t$ $\cos^{-1} -1=8\pi t$ $\pi=8\pi t$ $8\pi t=\pi$ $t=\frac{\pi}{8\pi}=\frac{1}{8}$ seconds Therefore, the weight first reaches maximum height after $\frac{1}{8}$ seconds.