# What is the period of f(theta)= sin 4 t - cos 12 t ?

$\frac{\pi}{2}$
Period of sin t --> $2 \pi$
Period of sin 4t --> $\frac{2 \pi}{4} = \frac{\pi}{2}$
Period of cos t --> $2 \pi$
Period of cos 12t --> $\frac{2 \pi}{12} = \frac{\pi}{6}$
Common period for f(t) --> least multiple of $\frac{\pi}{2} \mathmr{and} \frac{\pi}{6}$ --> it is $\frac{\pi}{2}$