# How do you determine a periodic function with the following characteristics: amplitude = 3 and period = 4pi?

$\pm 3 \sin \left(\frac{t}{2} + c\right)$, where c is a constant.
The period of a sin kt is $\frac{2 \pi}{k}$ and the amplitude is $| a |$.
Check: Addition of period to t should amount to adding $2 \pi$ to the whole argument.