# Thread: Given the equation: y = 2+3cos(2x+pi/2), find the following:

1. ## Given the equation: y = 2+3cos(2x+pi/2), find the following:

a) Amplitude :

b) Vertical Shift:

c) Phase Shift:

d) Period:

2. ## Re: Given the equation: y = 2+3cos(2x+pi/2), find the following:

Okay, where are you having difficulty? Do you know the definitions of these things?

3. ## Re: Given the equation: y = 2+3cos(2x+pi/2), find the following:

I know that the amplitude is the absolute value, i think its either 2 or 3, isnt the vertical shift, left pi/2? And is the period 4? Because i know that period is 2pi/b

4. ## Re: Given the equation: y = 2+3cos(2x+pi/2), find the following:

I think you may understand but it is worded very poorly. "the amplitude is the absolute value". Absolute value of what? The "amplitude is the distance from the "middle value" to either the maximum or minimum values so it is half the maximum value minus the minimum value. What is that?

"isnt the vertical shift, left pi/2"? A vertical shift is up and down, not left or right! If you have found the maximum and minimum values, then the "vertical shift" is the middle value: half the maximum value plus the minimum value. What is that?

And is the period 4? Because i know that period is 2pi/b.
Okay, what is "b" in this problem? (No, it is not pi/2. That is a "horizontal shift".)

The period of sin(x) is 2pi: sin(x+ 2pi)= sin(x). Here, x is replaced by 2x+ pi/2. So if sin((2(x+ P)+ pi/2)= sin(2x+ pi/2), we must have 2(x+ P)+ \pi/2= 2x+ pi/2+ 2\pi. Solve that for P.