What is the period of #f(theta) = tan ( ( 13 theta)/4 )- cos ( ( 6 theta)/ 5 ) #?

1 Answer
Apr 18, 2018

#(20pi)/39#

Explanation:

#tanx# has a period of #pi#, while #cos x# has a period of #2pi#

Thus #tan((13theta)/4)# completes one period, when #theta# changes by #(4pi)/13#, while

#cos((6pi)/5)# repeats when #theta# changes by #(5pi)/3#

So, the period of #f(theta)# is the least common multiple of #(4pi)/13# and #(5pi)/3#, i.e. #(20pi)/39#