Answer
$E(t)=219.2 cos(200\pi t)$ and $RMS=219.2V$
Work Step by Step
Step 1. Identify the quantities as $f=100rps, V_{max}=310$, thus we get $\frac{\omega}{2\pi}=100$ which gives
$\omega=200\pi$. The RMS voltage (see Example 6) is given by $\frac{V_{max}}{\sqrt 2}=\frac{310}{\sqrt 2}=219.2$ volt.
Step 2. Model with a cosine function $E(t)=a\cdot cos(\omega t)$ where $a=RMS=219.2$ we have
$E(t)=219.2 cos(200\pi t)$ (assuming t=0, E(0)=219.2V)
