Q: Consider the function y = -5 cos (2x – .1*pi)
a) Identify the amplitude
b) Identify the phase shift
c) Identify the period
Answer:
The following formulas / concepts will work for sin and cos graphs:
y = a cos (b*(x – h) ) + k
Note: a, b, h and k are just numbers that will affect the graph.
The amplitude is |a|
The phase shift if 2*pi / |b|
The phase shift is “h”
The vertical shift is “k”
A big thing to notice: the “b” value is factored out in this formula.
So…. Let’s start with our actual example: y = -5 cos (2x – .1*pi)
Identify who is a, b, h, and k. Notice, the b is not factored out, so let’s do that firt:
y = -5 cos (2x – .1*pi)
y = -5 cos (2*(x – .05*pi))
[if you multiply the 2 back through, you get the same as the original]
Now,
a = -5
b = 2
h = .05*pi
k = 0 (there is no + k at the end of the problem)
a) The amplitude is |a| = |-5| = 5
b) The phase shift is h = .05*pi (the graph is shifted .05*pi units to the right)
c) The period is 2*pi/|b| = 2*pi/|2| = pi