Question

What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?

Answer 1

The period of cos is 2π
so the period of cos(4x + π) is 2π/4 = π/2
cos(4x + π) = -cos4x => -3 cos(4x + π) + 6 = 3cos4x + 6
phase shift may be [-π/4,π/4]
amplitude is [-3,3]

Answer 2

amplitude = 3

period = π/2

phase shift: x = -π/4

Explanation:

Given:

f(x) = −3 cos(4x + π) + 6

which has the general form:

f(x) = A cos(Bx - C) + D

with:

A = -3

B = 4

C = -π

D = 6

The amplitude, period and phase shift is calculated as follows:

amplitude = |A| = |-3| = 3

period = 2*π/|B| = 2*π/|4| = π/2

phase shift: C/B = -π/4