What is the period of #f(theta)= sin 15 t - cos t #?

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Answer 1 · 2016-05-07T16:51:29

#2pi#.

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

So, the separate periods for #sin 15t and -cos t are #(2pi)/15 and 2pi.

As #2pi# is 15 X (2pi)/15,

#2pi# is the period for the compounded oscillation of the sum.

#f(t+2pi)=sin (15(t+2pi))-cos(t+2pi)#

#= sin (15t+30pi))-cos(t+2pi)#

#=sin 15t-cos t#

= f(t).