How do you find the amplitude, period and phase shift for #y = 2 cos (x/2 - Pi/6)#?

2 Answers
Jul 29, 2015

#y = 2cos (x/2 - pi/6)#

Explanation:

Amplitude: (-2, 2)
Period of cos x is #2pi# --> period of #x/2# is #4pi.#
Phase shift: #-pi/6#

Jul 29, 2015

There are several steps.

Explanation:

The form of this equation is

#y = Acos(Bx+C)" "# or #" "y=Acos(Bx-C)#

(Some textbooks use the first, others use the second.)

The Amplitude is #abs(A)#

Period can be found by #(2pi)/B#

Phase Shift is found by solving:
#Bx+C = 0" "# (or #Bx-C = 0" "# depending on textbook.)

For #y = 2cos(x/2-pi/6)#, note that we can write this as:

#y = 2cos(1/2x-pi/6)" "# (so it is clear that #B = 1/2#)

Amplitude: #" " 2#

Period: # " "4pi#

Found by simplifying #(2pi)/(1/2) = (2pi)/1 * 2/1 = 4pi#

Phase Shift: #" " pi/3#

Found by solving: #x/2-pi/6 = 0# so #x/2 = pi/6# and # x = (2pi)/6 = pi/3#