Answer:
Step-by-step explanation:
This is your function:
[tex]y=3cos\frac{1}{4}(\theta+\frac{\pi }{3})-2[/tex] 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
[tex]y=3cos(\frac{1}{4}\theta+\frac{\pi }{12})-2[/tex]
The formula to find the period is [tex]\frac{2\pi }{n}[/tex] and our n value is 1/4. So the period is found in
[tex]\frac{2\pi }{\frac{1}{4} }[/tex] or
[tex]2\pi *\frac{4}{1}=8\pi[/tex]
