Question

Consider the trigonometric function f(x)=4cos(2x pi/2) +9

How do you determine the minimum and maximum values of this function?

Answer 1

Max and Min:

Max = 13

Min = 5

COS Standard Period

`2\pi`

COS Period with a multiplier of 2 on x

`\pi`

COS Period with a multiplier of 2 on x and a Phase Shift

Answer to period

`(5)/(4)\pi`

Explanation:

Please view the image I have provided.

Answer 2

Make use of your knowledge of the maximum and minimum of the cosine function. Then scale and translate according to the way that function is scaled and translated to make f(x).

Explanation:

f(x) is the cosine function, multplied by 4 and with 9 added to the result.

The minimum of the cosine function is -1. Multiplying that by 4 gives -4, and adding 9 gives 5.

The maximum of the cosine function is +1. Multiplying that by 4 gives +4, and adding 9 gives 13.

The minimum and maximum of f(x) are 5 and 13, respectively.