## A community for students. Sign up today!

Here's the question you clicked on:

## kenneyfamily 2 years ago PLEASE HELP y=2cos(x/4+pi)-1 find period, phase shift, and vertical shift

• This Question is Closed
1. tkhunny

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.

2. kenneyfamily

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

3. tkhunny

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.

4. kenneyfamily

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

5. tkhunny

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.

6. kenneyfamily

is it 1? i know im sorry @tkhunny

7. tkhunny

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.

8. kenneyfamily

pi/4

9. tkhunny

Is that the answer or are you guessing? $$\dfrac{x}{4} + \pi = \dfrac{1}{4}(x + 4\pi)$$

10. kenneyfamily

i was guessing, but its 4pi

11. kenneyfamily

thank you so much

12. tkhunny

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

#### Ask your own question

Ask a Question
Find more explanations on OpenStudy