Question

How do you find the amplitude and period for `y=3cosx+2`?

Answer 1

`"amplitude"=3," period " =2pi`

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 = 0 and d =2

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