Question

What are the phase shift and period for the function y equals three cosine start fraction one over four end fraction (theta plus sixty degrees end power )minus two?

Answer 1

Explanation:

This is your function:

`y=3cos(1)/(4)(\theta+(\pi )/(3))-2` written in terms of pi instead of degrees. The phase shift is apparent from this form. The function is being shifted pi/3 radians or 60 degrees to the right. Finding the period requires us to distribute in the 1/4 to get

`y=3cos((1)/(4)\theta+(\pi )/(12))-2`

The formula to find the period is
`(2\pi )/(n)` and our n value is 1/4. So the period is found in

`(2\pi )/((1)/(4) )` or

`2\pi *(4)/(1)=8\pi`