How do you find the amplitude, period, and phase shift of 4cos(3theta + 3/2pi) + 2?

1 Answer
Jun 4, 2015

First, the range of the cosinus function is [-1;1]
rarr therefore the range of 4cos(X) is [-4;4]
rarr and the range of 4cos(X)+2 is [-2;6]

Second, the period P of the cosinus function is defined as: cos(X) = cos(X+P) rarr P = 2pi.
rarr therefore:

(3theta_2+3/2pi)-(3theta_1+3/2pi) = 3(theta_2-theta_1) = 2pi

rarr the period of 4cos(3theta+3/2pi)+2 is 2/3pi

Third, cos(X)=1 if X=0
rarr here X=3(theta+pi/2)
rarr therefore X=0 if theta = -pi/2
rarr therefore the phase shift is -pi/2