Trigonometric Functions

Question

Identify the amplitude, period, phase shift and vertical shift (mean value over one period) of:


f(x)=−5cos(4πx−12π)+3
 

(π is pi)

Answer 1

The general form for a cosine (or other trig function) function is:

 

f(x) = a·cos(b(x-c)) + d

 

Where:

• a = amplitude
• b = 2pi/period, so period = 2pi/b
• c = horizontal or phase shift
• d = vertical shift

 

First, we must put your function into that form:

 

f(x) = −5·cos(4πx−12π) + 3

f(x) = −5·cos(4π(x−3)) + 3

 

• a = amplitude = -5
• b = 4pi = 2pi/period; so period = 2pi/4pi = 1/2
• c = phase shift = 3
• d = vertical shift = 3