Question

How do you find the amplitude, period and phase shift for `y=3cos(theta-pi/3)`?

Answer 1

`3,2pi,pi/3`

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" and vertical shift " =d`

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

`rArr"amplitude " =|3|=3," period " =(2pi)/1=2pi`

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