Question

How do you find the amplitude, period, phase shift given `y=1+8cos(6x-pi)`?

Answer 1

`8,pi/3,pi/6`

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 = 8 , b = 6 ,c`=-pi` and d = 1

Hence amplitude `=|8|=8,"period" =(2pi)/6=pi/3`

`"phase shift" =-(-pi)/6=pi/6`

`"vertical shift" =1=((0),(1))`