What is the period of #f(t)=sin( t / 32 )+ cos( (t)/16 ) #?

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Answer 1 · 2016-07-01T07:16:06

#64pi#

The period for both sin kt and cos kt is #2pi$.

Separate periods for sin(t/32) and cos (t/16) are #64pi and 32pi#.

So, the compounded period for the sum is the LCM of these two

periods# = 64pi#.

#f(t+64pi)=sin ((t+64pi)/32)+cos((t+64pi)/16)#

#=sin(t/32+2pi)+cos(t/16+4pi)#

#-sin(t/32)+cos(t/16)#

#=f(t)#