Answer
$\theta(t)=10sin(\pi t)$
Work Step by Step
Step 1. Identify the quantities as: $p=2s, |a|=10^\circ, \theta(0)=0$ where $\theta(0)=0$ means that the angle is 0 at the starting point t=0.
Step 2. Use a sine function to model the change of angle as $\theta(t)=|a|sin(\omega t)$, with $p=\frac{2\pi}{\omega}=2$, we have $\omega=\pi$ and the equation becomes $\theta(t)=10sin(\pi t)$
Step 3. Check the correctness of the equation: at $t=0s, \theta(0)=0^\circ$, at $t=0.5s, \theta(0.5)=10^\circ$ (quarter cycle).
