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

1 Answer
Aug 30, 2016

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#