may i get assistance with this

Question

the period of the function y=3cos(4x-π) is

 

1.) 2π

 

2.) -π

 

3.) not a periodic function

 

4.) 4π

 

5.) π

 

6.) π/2

Answer 1

Hi Corey,

 

y=3cos(4x-π)

 

y=3cos4(x-π/4)

 

Here, b=4

 

The period of the function=2π/b

 

                                     =2π/4

 

                                      =π/2

 

So the answer is (6) =π/2

Answer 2

y=3cos(4x-π)

 

θ = 4x - pi

 

y = 3cos(θ) has one period on the interval 0 ≤ θ < 2pi.

 

So y = 3cos(4x - pi) has one period on the interval 0 ≤ 4x - pi < 2pi,
or pi ≤ 4x < 3pi, or pi/4 ≤ x < 3pi/4.

 

The length of that period is 3pi/4 - pi/4 = 2pi/4 = pi/2.

 

The answer is 6.