How do you find the amplitude, period, vertical and phase shift and graph #y=3-1/2costheta#?

1 Answer
Jun 1, 2017

Amplitude: #1/2#
Period: #2pi#
Vertical shift: #3#
Phase shift: #pi#

Explanation:

Given: #3 - 1/2cos(theta)#

Begin by observing that multiplication of a sinusoid by negative is a phase shift of #pi#

Using the general from,

#y = Acos(Btheta+C)+D#

The phase shift #phi = C/B#

In the given equation #B = 1#, therefore, we can rewrite the equation without a negative sign if we insert #pi# phase shift:

#pi = C/1#

#C = pi#

#y = 1/2cos(theta+pi)+3#

Period #T = (2pi)/B#

#T = 2pi#

The amplitude is #A = 1/2#

Vertical shift #D = 3#