Chapter 6 - 6.7 - Applications and Models - 6.7 Exercises - Page 497: 55c

$t=\frac{\pi}{32}~second\approx0.0982~second$

The first value of $x\gt0$ which gives us $cos~x=0$ is $x=\frac{\pi}{2}$ $y=0$ $\frac{1}{4}~cos~16t=0$ $cos~16t=0$ $16t=\frac{\pi}{2}$ $t=\frac{\pi}{32}~second\approx0.0982~second$