What is the frequency of #f(theta)= sin 4 t - cos 24 t #?

1 Answer
Aug 10, 2018

#2/pi#

Explanation:

#f( t ) = sin 4t - cos 24t#

The separate frequencies for the two terms are

# F_1 =# reciprocal of the period #= 4/( 2pi) = 2/pi# and

#F_2 = 24/(2pi) = 12/pi.

The frequency F of #f ( t )# is given by

#1/F = L/F_1 = M/F_2, for befitting integers L and M, givnig

Period #P = 1/F = Lpi/2 = Mpi/12#.

Note that 2 is a factor of 12.

Easily, the lowest choice is L = 1, M = 6 and

#P = 1/F = pi/2# giving #F = 2/pi#.