Question

How do you find the amplitude and period of `y=1/2cos(3/4theta)`?

Answer 1

`"amplitude "=1/2," period "=(8pi)/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=1/2,b=3/4,c=0,d=0`

`rArr"amplitude "=|1/2|=1/2" and period "=(2pi)/(3/4)=(8pi)/3`