Question

What is the amplitude, period and the phase shift of `y= 5/2 cos (x/2)`?

Answer 1

amplitude `=5/2`
period `=4pi`

Explanation:

The standard form of the cosine function is.

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=acos(bx+c)+d)color(white)(a/a)|)))`

where amplitude = |a| , period `=(2pi)/b`

phase shift `=-c/b" and vertical shift" =d`

here a `=5/2` , b `=1/2` , c = 0 and d = 0

Hence amplitude `=|5/2|=5/2` and period `=(2pi)/(1/2)=4pi`