What is the period of #f(theta) = tan ( ( 5theta)/12 )- cos ( ( 5 theta)/ 4 ) #?

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Answer 1 · 2018-05-13T08:14:52

The period is #=24/5pi#

The period of the sum of #2# periodic functions is the LCM of their periods.

The period of #tan(5/12theta)# is

#T_1=(pi)/(5/12)=12/5pi#

The period of #cos(5/4theta)# is

#T_2=(2pi)/(5/4)=8/5pi#

The LCM of #12/5pi# and #8/5pi# is

#T=24/5pi#

graph{tan(5/12x)-cos(5/4x) [-20.27, 20.29, -10.14, 10.13]}