What is the frequency of #f(theta)= sin 6 t - cos 45 t #?

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Answer 1 · 2017-05-31T11:55:08

The frequency is #=3/(2pi)#

We start by calculating the period of

#f(t)=sin6t-cos45t#

The period of the sum (or difference) of #2# periodic functions is the LCM of their periods

The period of #sin6t# is #=2/6pi=1/3pi#

The period of #cos45t# is #=2/45pi#

The LCM of #1/3pi# and #2/45pi# is

#=30/45pi=2/3pi#

So,

#T=2/3pi#

The frequency is

#f=1/T=3/(2pi)#