Question

PLEASE HELP
y=2cos(x/4+pi)-1

find period, phase shift, and vertical shift

Answer 1

Well, do it.

\(y = \cos(x)\)
Amplitude: 1
Period: \(2\pi\)
Phase Shift: 0
Vetical Shift: 0

\(y = 2\cos(x)\)
Amplitude: 2
Period: \(2\pi\)
Phase Shift: 0
Vetical Shift: 0

\(y = 2\cos(x) - 1\)
Amplitude: 2
Period: \(2\pi\)
Phase Shift: 0
Vetical Shift: -1

You do the rest.

Answer 2

sorry could you please explain further? i am confused @tkhunny

Answer 3

Yes I can, but you need to get unconfused. Each piece means something. I showed you the basic functino, the Amplitude, and the Vertical Shift (outside of the function argument). Now, you go find the Phase Shift and the Period. Hint, they are inside the function argument.

Answer 4

period is pi/2? or 2pi. and phase shift is either pi/4 or 4 pi. i think. sorry i am trying to follow @tkhunny

Answer 5

It helps a LOT if you organize and keep track of everything. In my version, I added one thing in the function and changed one thing in the list.

\(y=2\cos(x/4)−1\)
Amplitude: 2
Period: \(8\pi\)
Phase Shift: 0
Vetical Shift: -1

One more... Don't make me do all the work.

Answer 6

is it 1? i know im sorry @tkhunny

Answer 7

Seriously, stop apologizing and focus on what you are doing. This is really just a memorization problem. There isn't anything magic about it.

\(y = a\cos(b(x-c))+d\)

Either you know or you don't.

Amplitude: a
Vertical Shift: d
Period: \(2\pi/b\) <== For cosine, anyway.
Phase Shift: c

Now, work inside that argument, \(x/4 + \pi\), and use the distributive property to factor out 1/4 and you should find the Phase Shift staring at you.

Answer 8

pi/4

Answer 9

Is that the answer or are you guessing?

\(\dfrac{x}{4} + \pi = \dfrac{1}{4}(x + 4\pi)\)

Answer 10

i was guessing, but its 4pi

Answer 11

thank you so much

Answer 12

Now, you do another one. You made me do ALL of that one. Encourage me that youcan do it on your own.