# What is the period of f(theta) = tan ( theta) - cos ( (2 theta)/9) ?

$18 \pi$.
The period of both$\tan k \theta \mathmr{and} \cos k \theta$ is $\frac{2 \pi}{k}$
The separate periods of the two terms in f(x) are $2 \pi \mathmr{and} 9 \pi$.
So, the compounded period for the sum is LCM of (2.9) X $\pi = 18 \pi$.