Question

What is the period of `f(theta) = tan ( ( 8 theta)/9)- sec ( ( 3 theta)/ 8 )`?

Answer 1

`144pi`

Explanation:

Period of `tan ((8t)/9)` --> `9(pi)/8`
Period of `sec ((3t(/8)` --> `8(2pi)/3 = (16pi)/3`
Find least common multiple of `(9pi)/8 and (16pi)/3`

`(9pi)/8` ...x (8)(16) ...--> `144pi`
`(16pi)/3` ... x ((3)(9) ...--> `144pi`

Period of f(t) --> `144pi`