Question

How do you find the period and amplitude of `y=5/2cos(x/4)`?

Answer 1

`"period "=8pi" and amplitude "=5/2`

Explanation:

`"the standard form of the 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=5/2,b=1/4,c=d=0`

`"amplitude "=|5/2|=5/2," period "=(2pi)/(1/4)=8pi`