What is the frequency of #f(theta)= sin 24 t - cos 15 t #?

Question

1385 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-19T08:35:04

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

Let 's calculate the period #T#

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

The period of #sin24t# is #=2/24pi=pi/12#

The period of #cos15t# is #=2/15pi#

The multiples of #pi/12# are

#{pi/12 , 2/12pi, 3/12pi, 4/12pi,5/12pi, 6/12pi,7/12pi,color(red)(8/12pi),9/12pi...}#

The multiples of #2/15pi# are

#{2/15pi,4/15pi,6/15pi, 8/15pi,color(red)(10/15pi),12/15pi}#

The #LCM# of #pi/12# and #2/15pi# is

#8/12pi=2/3pi#

So,

#T=2/3pi#

and the frequency is

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