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anonymous

  • one year ago

What are the amplitude, period, phase shift, and midline of f(x) = -3 sin(4x - π) + 2? (5 points)

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  1. anonymous
    • one year ago
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    @Owlcoffee

  2. anonymous
    • one year ago
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    http://gyazo.com/79c729685b340c46e3861aac421894b3

  3. freckles
    • one year ago
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    what do you think the amp is?

  4. freckles
    • one year ago
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    that is all you really have to know to get this question

  5. anonymous
    • one year ago
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    how do i find it

  6. freckles
    • one year ago
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    oh I thought you would know how because it is the easiest thing to find it is the absolute value of the constant number being multiplied to the trig function there

  7. anonymous
    • one year ago
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    so 3?

  8. freckles
    • one year ago
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    yep

  9. freckles
    • one year ago
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    you are done because there is only one option with amp=3

  10. anonymous
    • one year ago
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    lol yay thanks

  11. anonymous
    • one year ago
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    http://gyazo.com/0060f7a559b9d1fb6d4bef7b957a2c03 is that answer right

  12. Owlcoffee
    • one year ago
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    in any trigonometric equality with the form: \[y=Asin(ax+ \alpha) \] The amplitude is the number "A" and you can calculate the period with: \[p=\frac{ 2 \pi }{ a }\]

  13. freckles
    • one year ago
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    you mean the amp=|A|?

  14. freckles
    • one year ago
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    \[y=A \sin(bx+c)+d \\ \text{ amp } =|A| \\ \text{ period } =\frac{2 \pi}{|b|} \\ \\ \text{ phase shift : } \text{ solve for } x : bx+c=0 \\ \text{ max if } A \text{ is } \text{ positive is } A(1)+d=A+d \\ \text{ min if } A \text{ is } \text{ positive is } A(-1)+d=-A+d \\ \text{ so the average the of max and min is }=\frac{(A+d)+(-A+d)}{2}=\frac{2d}{2}=d \\ \text{ the midline is therefore } y=d\]

  15. anonymous
    • one year ago
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    thank you for all of that

  16. anonymous
    • one year ago
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    was my answer correct for the other 1?

  17. freckles
    • one year ago
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    oh yep you can apply the same information I just gave to that one you have period is 2pi 2pi=2pi/|b| means |b|=1 which means b=-1 or b=1 phase shift (think horizontal shift): solve inside=0 to get phase shift and as you see x-pi=0 gives x=pi so pi is the phase shift the vertical shift is yes the number hanging outside the d=-4

  18. anonymous
    • one year ago
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    yay thank you :)

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