What is the period of #f(t)=sin( t / 30 )+ cos( (t)/ 12 ) #?

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Answer 1 · 2016-07-28T05:35:12

#120 pi#

The period for both #sin kpi and cos kpi is #(2pi)/k#.

Here, the separate periods for terms in f(t) are #60pi and 24pi#

So, the period P for the compounded oscillation is given by

P = 60 L = 24 M, where L and M together form the least possible pair

of positive integers. L= 2 and M = 10 and the compounded period

#P = 120pi #.

See how it works.

#f(t+P)#

#=f(t+120pi)#

#=sin (t/30 + 4pi) + cos (t/12 + 10pi)#

#=sin(t/30)+cos(t/12)#

#=f(t).

Note that #P/20 = 50pi# is not a period, for the cosine term.