Posted by **Kasey** on Wednesday, December 17, 2008 at 5:09pm.

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

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

- Trig help -
**Reiny**, Wednesday, December 17, 2008 at 5:54pm
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

- Correction on Trig help -
**Reiny**, Wednesday, December 17, 2008 at 5:55pm
last line should have said:

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

(keystroke error)

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