# What is the period of f(theta)= sin 7 t - cos 5 t ?

$2 \pi$
Period of sin (7t) --> $\frac{2 \pi}{7}$
Period of cos (5t) --> $\frac{2 \pi}{5}$
Period of f(t) --> least common multiple of (2pi)/7 and (2pi)/5 --> $2 \pi$
$\frac{2 \pi}{7}$ x (7) --> $2 \pi$
$\frac{2 \pi}{5}$ x (5) --> $2 \pi$