precalc question

Question

Let .

What is the amplitude?  

What is the period?  

What is the phase shift?  

[NOTE: If needed, you can enter  as 'pi' in your answers.]

Answer 1

y = -3•cos [3(x-π/4)]

For cosine function, consider this form:

y = a•cos [b(x-c)] + d

Where

|a| = amplitude

2π/b = period

c = phase shift

d = vertical shift

from the parent function y = cos x.

Given in the problem:

a = -3

b= 3

c = π/4

d = 0 (which we don't need)

(1) For amplitude: |a| = |-3| = 3

(2) For period: 2π/b = 2π/3

(3) For phase shift: c = π/4 (to the right)