Answer
From the graph, we can see that $P \leq 0$ on the interval $[0.001638,~0.003549]$
Work Step by Step
$P=0~~$ when $~~2\pi(261.63)t+\frac{\pi}{7} = \pi~n$, where $n$ is an integer.
$t = \frac{7n-1}{(2)(261.63)(7)}$
$t = \frac{7n-1}{3662.82}$
We can find the first positive value of $t$ such that $P=0$:
$t = \frac{(7)(1)-1}{3662.82}$
$t = 0.001638~s$
We can find the second positive value of $t$ such that $P=0$:
$t = \frac{(7)(2)-1}{3662.82}$
$t = 0.003549~s$
From the graph, we can see that $P \leq 0$ on the interval $[0.001638,~0.003549]$
