# What is the period of f(theta)= sin 4 t - cos 5 t ?

$2 \pi$
Period of sin (4t) --> $\frac{2 \pi}{4} = \frac{\pi}{2}$
Period of cos (5t) ---> $\frac{2 \pi}{5}$
Least common multiple of $\frac{\pi}{2} \mathmr{and} \frac{2 \pi}{5} - \to 2 \pi$
Period of f(t) --> $2 \pi$