What is the frequency of #f(theta)= sin 6 t - cos 21 t #?

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Answer 1 · 2016-08-12T12:27:22

#3/(2pi)=0.4775#, nearly.

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

The periods for the separate oscillations #sin 6t and - cos 21t# are

#pi/3 and (2pi)/21#, respectively.

Twice the first is seven times the second. This common value

(least) # P = (2pi)/3) is the period for the compounded oscillation f(t).

See how it works.

#f(t+P)#

#=f(t+(2pi)/3)#

#=sin((6t+4pi)-cos(21t+14pi)#

#=sin 6t-cos 21t#

#=f(t).

Note that P/2 used instead of P changes the sign of the second

term. .

Frequency is 1/P..