Question

How do you find the amplitude and period of a function `y= -4 cos 2x`?

Answer 1

`"amplitude "=4," period"=pi`

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=-4,b=2,c=0,d=0`

`rArr"amplitude "=|-4|=4" and period "=(2pi)/2=pi`