What is the period of #f(theta) = tan ( ( 5theta)/12 )- cos ( ( 2 theta)/ 3 ) #?

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Answer 1 · 2016-07-23T09:59:08

#12pi#

The period of #tan ktheta # is #pi/k#

and the period of #cos ktheta# is #(2pi)/k#.

So, here,

the separate periods of the two terms in #f(theta)# are

#(12pi)/5 and 3pi#.

For #f(theta)#, the period P is such that #f(theta+P)=f(theta)#,

both the terms are become periodic and P is the least possible such

value.

Easily, #P =5(12/5pi)=4(3pi)=12pi#

Note that, for verification,

#f(theta+P/2)=f(theta+6pi)# is not #f(theta)#, whereas

#f(theta+nP)=f(theta+12npi)=f(theta), n=1, 2, 3,..#