Determine the a amplitude b period c phase change d equation

Determine the (a.) amplitude (b.) period (c.) phase change (d.) equation for the midline For the following trig equations. Y= -1/2 cos(2x + pi/4) y = 3sin(1/2x - pi/2) + 1 y = -5sin(pix) + 2

Solution

1)y =-(1/2)cos(2x +/4) comparing with y =Asin(Bx+C)

amplitude =A=1/2

period =2/B=2/2 =

phase change =-C/B=-(/4)/2 =-/8

midline is y =0

2)y =3sin((1/2)x -/2)+1

amplitude =2

period =2/(1/2) =4

phase change =-(-/2)/(1/2) =

maximum value =3+1=4, minimum value =-3+1=-2

midline is y =(4-2)/2=> y=1

3)y =-5sin(x) +2

amplitude =5

period =2/() =2

phase change =0

maximum value =5+2=7, minimum value =-5+2=-3

midline is y =(7-3)/2=> y=2