What is the period of #f(t)=sin( t / 30 )+ cos( (t)/ 33) #?

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Answer 1 · 2016-07-28T08:28:41

#660pi#

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

So, the separate periods for the the two terms in f(t) are

#60pi and 66pi#

The period for the compounded oscillation of f(t) is given by

least positive integer multiples L and M such that

the period P = 60 L = 66 M.

L = 11 and M =10 for P =660#pi#.

See how it works.

#f(t+P)#

#=f(t+660pi)#

#=sin(t/30+22pi)+cos(t/33+20pi)#

#=sin(t/30)+cos(t/33)#

#=f(t)#.

Note that, #P/2 = 330pi# is not a period, for the sine term.