What is the frequency of #f(t)= sin 3 t - cos 27 t #?

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Answer 1 · 2016-08-30T16:41:37

#1/(2pi)#

Frequency is the reciprocal of the period.

The period of both sin kt and cos kt is #2/kpi#. So,

the separate periods for

#sin 3t and cos 27t#

are

#2/3pi and 2/27pi#. The period P for

#f(t)=sin 3t-cos 27t# is given by

#P=M(2/3pi)=N(2/27)pi#, where M and N are positive giving P

as the least positive-even-integer-multiple of #pi#.

Easily, M = 3 and N = 27, giving #P = 2pi#.

The frequency #= 1/P = 1/(2pi)#.