# What is the period of f(theta) = tan ( ( 12 theta)/7 )- sec ( ( 7 theta)/ 6 ) ?

##### 1 Answer
May 18, 2018

$84 \pi$

#### Explanation:

Period of $\tan \left(\frac{12 t}{7}\right) - \to \frac{7 \pi}{12}$
Period of $\sec \left(\frac{7 t}{6}\right) - \to 6 \frac{2 \pi}{7} = \frac{12 \pi}{7}$
Period of f(t) --> least common multiple of $\frac{7 \pi}{12} \mathmr{and} \frac{12 \pi}{7}$

$\frac{7 \pi}{12}$ ......x...(12)(12) .... --> $84 \pi$
$\frac{12 \pi}{7}$.......x......(7)(7) ..... --> $84 \pi$

Period of f(t) is $84 \pi$