Amplitude, Period & Phase Shift of Trigonometric Equations

[nycmathguy]

 

[MathLover1]

1.

y=3cos(2x-pi)

for f (x )=A*(Bx-C)+D, where

A=amplitude
B=period
C/B=phase shift
D=vertical shift

B=2, C=pi, D=0
periodicity of cos (x ) is 2pi

so,

amplitude: 3

period: periodicity/B=2pi/2=pi

phase shift: pi/2


2.

y=-4sec(4x-3pi/2)

B=2, C=3pi/2, D=0
periodicity of sec (x ) is 2pi
function sec (x ) doesn't have amplitude

so,

amplitude: none

period: periodicity/B=2pi/2=pi

phase shift: C/B=(3pi/2)/2=3pi/4

 

[nycmathguy]

1.

y=3cos(2x-pi)

for f (x )=A*(Bx-C)+D, where

A=amplitude
B=period
C/B=phase shift
D=vertical shift

B=2, C=pi, D=0
periodicity of cos (x ) is 2pi

so,

amplitude: 3

period: periodicity/B=2pi/2=pi

phase shift: pi/2


2.

y=-4sec(4x-3pi/2)

B=2, C=3pi/2, D=0
periodicity of sec (x ) is 2pi
function sec (x ) doesn't have amplitude

so,

amplitude: none

period: periodicity/B=2pi/2=pi

phase shift: C/B=(3pi/2)/2=3pi/4

Pretty easy. This is a walk down memory lane.
There are three more threads in this forums for you to play with. I will not post new threads until all questions have been answered or at least hints provided.