Question

What is the phase shift, vertical displacement with respect to `y=cosx` for the graph `y=cos(x-pi/3)`?

Answer 1

`" shift of " pi/3to" no vertical displacement"`

Explanation:

The standard form of the `color(blue)"cosine function"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=acos(bx+c)+d)color(white)(2/2)|)))`

`"where amplitude " =|a|," period " =(2pi)/b`

`"phase shift " =-c/b," vertical displacement " =d`

`"here " a=1,b=1,c=-pi/3,d=0`

`rArr"phase shift "=-(-pi/3)/1=pi/3`

`"with respect to " y=cosx`

`y=cos(x-pi/3)" is " y=cosx" shifted " pi/3" to the right"`