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kenneyfamily

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

  • one year ago
  • one year ago

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  1. tkhunny
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    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.

    • one year ago
  2. kenneyfamily
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    sorry could you please explain further? i am confused @tkhunny

    • one year ago
  3. tkhunny
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    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.

    • one year ago
  4. kenneyfamily
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    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

    • one year ago
  5. tkhunny
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    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.

    • one year ago
  6. kenneyfamily
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    is it 1? i know im sorry @tkhunny

    • one year ago
  7. tkhunny
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    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.

    • one year ago
  8. kenneyfamily
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    pi/4

    • one year ago
  9. tkhunny
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    Is that the answer or are you guessing? \(\dfrac{x}{4} + \pi = \dfrac{1}{4}(x + 4\pi)\)

    • one year ago
  10. kenneyfamily
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    i was guessing, but its 4pi

    • one year ago
  11. kenneyfamily
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    thank you so much

    • one year ago
  12. tkhunny
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    Now, you do another one. You made me do ALL of that one. Encourage me that youcan do it on your own.

    • one year ago
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