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What is the frequency of #f(theta)= sin 7 t - cos 3 t #?

Answer 1

Emery Adkins

#1/(period) = 1/(20pi)#.

The periods of both sin kt and cos kt is #2pi#.

So, the separate periods of oscillation by

#sin7t and cos 3t# are #2/7pi and 2/3pi#, respectively.

The compounded oscillation #f = sin 7t-cos 3t#, the period is given

P = (LCM of 3 and 7)#pi =21pi #.

A cross check:

#f(t+P)=f(t)# but #f(t+P/2) ne f(t)#

The frequency #= 1/P = 1/(20pi)#.

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Answer 2

Delilah Aguilar

To find the frequency of ( f(\theta) = \sin(7t) - \cos(3t) ):

The frequency of a trigonometric function is determined by the coefficient of ( t ) within the function.

For ( \sin(7t) ), the frequency is ( 7 ). For ( \cos(3t) ), the frequency is ( 3 ).

Therefore, the frequency of the function ( f(\theta) = \sin(7t) - \cos(3t) ) is determined by the highest frequency term, which is ( 7 ).

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