Question

Please find amplitude period and phase shifty=4cos(2x-pi/4)

Answer 1

• Amplitude: 4

,

• Period: π

,

• Phase shift: -π/8 (to the right)

Step-by-step explanation

The generic equation for a cosine function is:

`y=A\cos (B(x+C))+D`

where

• A is the amplitude

,

• 2π/B is the period

,

• C is the phase shift to the left (if it's negative, then it's to the right)

,

• D is the vertical shifit

In this equation:

`y=4\cos (2x-(\pi)/(4))`

We have to rewrite it so that it looks like the equation above. We take 2 as a common factor inside the cosine expression:

`y=4\cos (2(x-(\pi)/(8)))`

Now we clearly can see that

• A = 4

,

• C = -π/8

,

• D = 8

,

• B = 2 so the period is 2π/2 = π