What is the period of #f(t)=sin( t / 12 )+ cos( (t)/21 ) #?

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Answer 1 · 2016-05-11T12:20:20

#168pi#.

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

Here, the separate periods of oscillation of the waves

#sin (t/12) and cos (t/21)# are #24pi and 42pi#.

So, the period for the compounded oscillation for the sun is the

#LCM = 168pi#.

You see how it works.

#f(t+168pi)=sin ((1/12)(t+168pi)) + cos ((1/21)(t+168pi))#

#= sin (t/12+14pi)+cos (t/21+8pi)#

#=sin(t/12)+cos(t/21)#

#=f(t)#.