Question

Which of the following cosine functions has a period of 3Pi

Answer 1

C

Explanation:

Hello!

In the equation y=a cos bx, we can learn alot about the cosine graph.

a is the amplitude, or how 'long' the cosine graph is.

b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.

In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.

To find the period, we can plug b into
`(2\pi )/(b)` , which in a way converts the b value to a period.

For B) y= cos3x

`(2\pi )/(3)`= it does not equal 3
`\pi`

For C) y=cos
`(2)/(3)`x

`(2\pi )/((2)/(3))`= equals 3
`\pi` when simplified

Since C equals 3
`\pi` as a period, C is the only logical answer.