How would I state the phase shift of y=cos(θ-pi/3) & then graph it?

Question

Step by step would be awesome, I was out sick and needed to do a worksheet to catch up!

Answer 1

first make a sketch of y=cosθ
then translate it pi/3 radians to the right

in general for y=cos(θ-k) move y=cos(θ)to the right k radians

or for y=cos(θ+k) move y=cos(θ)to the left k radians

if there is a coefficient in front of the angle you have to factor out that coefficient to show the phase shift

e.g. y=cos(3θ-pi/2)
becomes y=cos3(θ-pi/6) , so the phase shift is pi/5 to the right

Answer 2

last line should have said:

becomes y=cos3(θ-pi/6) , so the phase shift is pi/6 to the right

(keystroke error)