How do you graph and list the amplitude, period, phase shift for #y=1/2cos(pi/4(x-2))+4#?

1 Answer
Aug 12, 2018

cos values #in [ - 1, 1 ]#

#y = 1/2 cos (pi/4 ( x - 2 )) + 4 in [ 4 - 1/2, 4 + 1/2 ] = [ 7/2, 9/2 ]#

Vertical shift = 4 rArr axis is # y = 4#.

Period = ( 2pi )/(pi/4) = 8

Amplitude = 1/2

Phase shift = 2

See graph,depicting all these aspects, for the simplified

#y = 1/2 sin(1/4pix) + 4#..
graph{(y-4-1/2 sin(1/4 pi x))(y-4+0x)(y-9/2+0x)(y-7/2+0x)=0[-10 10 3 6] }