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

Answer:

Step-by-step explanation:

This is your function:

$y=3cos\frac{1}{4}(\theta+\frac{\pi }{3})-2$ 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

$y=3cos(\frac{1}{4}\theta+\frac{\pi }{12})-2$

The formula to find the period is $\frac{2\pi }{n}$ and our n value is 1/4.  So the period is found in

$\frac{2\pi }{\frac{1}{4} }$ or

$2\pi *\frac{4}{1}=8\pi$