Question

Which of the following cosine functions has a period of 3 π ?

A. y = 3cosx
B. y = cos3x
C. y = cos2/3x
D. y = 1/3cosx

Answer 1

c. y= cos2/3x

Explanation:

Answer 2

C.

`y = \: \cos( (2)/(3)x )`

EXPLANATION

The period of a cosine function is calculated using the formula;

`T= (2 \pi)/(b)`

Therefore , if the period is 3π, then

`(2 \pi)/(b) = 3\pi`

We solve b to obtain,

`b = (2)/(3)`

This implies that, the given cosine function must have an equation of the form

`y = a \: \cos( (2)/(3)x )`

Among the options, the function in this form is:

`y = \: \cos( (2)/(3)x )`

The correct choice is C.