What is the frequency of #f(theta)= sin 12 t - cos 16 t #?

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Answer 1 · 2016-12-29T15:35:41

The frequency is #=2/pi#

The period of the sum of 2 periodic functions is the LCM of their periods.

The period of #sin12t# is #=2/12pi=4/24pi#

The period of #cos16t# is #=2/16pi=3/24pi#

#4=2*2#

#3=3*1#

LCM #(4,3)=3*2*2*=12#

The LCM of #pi/6# and #pi/8# is #=12/24pi=pi/2#

The period is #T=pi/2#

The frequency is #f=1/T#

#f=2/pi#