Question

find the phase shift, period and amplitude of the function:
y=1-2cos(2pix-3pi/2)

Answer 1

A general formula for the cosine function is y = a*cos (bx + c).
The AMPLITUDE of the function is the absolute value of ' a ': |a|.
The PERIOD of the function is 2Pi/b, where b is the coefficient of the variable x.
The PHASE SHIFT of the function is -c/b.

The graph of y=1-2cos(2pix-3pi/2) involves a vertical translation, but you are not asked about that. Thus, you can safely focus on just y=-2cos(2pix-3pi/2).

Answer 2

Using the formula I gave you, find the AMPLITUDE of this function.
What is the coefficient of x in this function? Once you have that, find the PERIOD.
What is ' c ' in this function? Once you have that, find the PHASE SHIFT.

Answer 3

amplitude 2

Answer 4

period is \[\frac{ 2\pi }{ 2 }\]

Answer 5

phase shift is \[-\frac{ 7\pi }{ 2 }\]

Answer 6

@mathmale

Answer 7

But I see that the coefficient of your x is 2pi, not just 2. Would you mind calculating the period again?

Answer 8

Also, I see that your ' c ' is -3pi/2.

if your ' b ' is 2pi,

What is your PHASE SHIFT, -c/b?

I need to get off the Internet, but will be back on later today. I'll look for your responses. Take care! mathmale

Answer 9

period is 1

Answer 10

that's better. What about that phase shift?

Answer 11

In summary: AMPLITUDE=2; PERIOD=1; PHASE SHIFT = ?

Answer 12

\[-\frac{ 3 }{ 4 }\]

Answer 13

Your ' c ' is -3Pi/2. What is -c? What is b?
What is your PHASE SHIFT, -c/b?

Answer 14

You were essentially right (about the PHASE SHIFT) the first time, but have a sign error there. Check that out. The phase shift in this problem is positive, not negative.

sorry, I need to go. But again, if you respond, I'll respond back, later on today.

Answer 15

3/4

Answer 16

that's right! So, you've successfully answered this question. Awesome.