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kenneyfamily

  • 2 years ago

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

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  1. tkhunny
    • 2 years ago
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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.

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

  3. tkhunny
    • 2 years ago
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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.

  4. kenneyfamily
    • 2 years ago
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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

  5. tkhunny
    • 2 years ago
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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.

  6. kenneyfamily
    • 2 years ago
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    is it 1? i know im sorry @tkhunny

  7. tkhunny
    • 2 years ago
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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.

  8. kenneyfamily
    • 2 years ago
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    pi/4

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

  10. kenneyfamily
    • 2 years ago
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    i was guessing, but its 4pi

  11. kenneyfamily
    • 2 years ago
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    thank you so much

  12. tkhunny
    • 2 years ago
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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.

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