What is the period of #f(t)=sin( t / 32 )+ cos( (t)/8 ) #?

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Answer 1 · 2016-08-11T07:29:30

#64pi#

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

Here, the separate periods for the oscillations

# sin(t/32) and cos (t/8#) are

#64pi and 16pi#, respectively.

The first is four times the second.

So, quite easily, the period for the compounded oscillation f(t) is

#64pi#

See how it works.

#f(t+64pi)#

#=sin(t/32+3pi)+cos(t/8+8pi)#

#=sin(t/32)+cos(t/8)#

#=f(t)#.
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