Question

How do you find the amplitude, period, phase shift for `y=cos(x+pi/2)`?

Answer 1

`"amplitude " =1," period" =2pi," phase shift" =-pi/2`

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=1,b=1,c=pi/2" and " d=0`

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

`"and phase shift " =-(pi/2)/1=-pi/2`