# What is the period of #f(theta) = tan ( ( 3 theta)/7 )- sec ( ( 5 theta)/ 6 ) #?

##### 1 Answer

If necessary, I would again edit my answer myself, for debugging.

#### Explanation:

Period of

Period of

Now,

the period of f( theta ), least possible

P = (7/3pi)L = (12/5pi)M.

If there is at least one term in the form

sine, cosine, csc or sec of

P = least possible ( P/2 not the period ).

integer multiple of

Let

Multiply by the LCM of the denominators in

= (3)(5) = 15. Then

As 35 and 36 are co-prime K = 1, N = (35)(36),

L = 36, M = 35, and P = 84

Verification:

If P is halved,

Graph, for one period,

,