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skullofreak

  • one year ago

help!!

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  1. skullofreak
    • one year ago
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  2. skullofreak
    • one year ago
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    how do I write the equation of the graph?

  3. alffer1
    • one year ago
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    Tell me what the graph of y = cos x looks like.

  4. skullofreak
    • one year ago
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    its (0,1) (pi,-1) (2pi,1) (3pi,-1) etc

  5. skullofreak
    • one year ago
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    but with the dots in um the up and down motions (from half of 0 and pi , pi and 2pi,

  6. alffer1
    • one year ago
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    So what is the difference between this one and cosx?

  7. skullofreak
    • one year ago
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    its sin ? and the graph is given but I don't know how to get an equation

  8. skullofreak
    • one year ago
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    nvm its cos

  9. ranga
    • one year ago
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    The sine function is zero when x = 0. A cosine function is 1 when x = 0. So we need to choose the acos(bx) here. a is the amplitude. Amplitude is how much above or how much below the mean line (which is x axis here) the curve swings. Could you figure out the amplitude from the diagram?

  10. skullofreak
    • one year ago
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    a = 3

  11. skullofreak
    • one year ago
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    so y = 3cos.. bx

  12. ranga
    • one year ago
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    Yes. a = 3. So the equation is y = 3cos(bx). We still need to figure out b. The period of a cosine or a sine function is how long before the curve repeats itself. Could you look at two successive peaks in the diagram and figure out after how much x the function repeats itself?

  13. skullofreak
    • one year ago
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    every 3pi?

  14. skullofreak
    • one year ago
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    or every 6pi/2?

  15. ranga
    • one year ago
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    No. The curve attains a peak at x = 0. The next peak occurs at x = 6pi. The period is how much x has passed before the curve starts to repeat itself. So what is the x distance between peak-to-peak?

  16. skullofreak
    • one year ago
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    6pi/2

  17. ranga
    • one year ago
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    No. At x = 0, first peak. At x = 6pi the next peak. The difference in x is: 6pi - 0 = 6pi. Every 6pi the curve repeats itself. You can take the distance between two successive low points also and it will still be 6pi. So the period of this curve is 6pi.

  18. skullofreak
    • one year ago
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    OH

  19. skullofreak
    • one year ago
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    y=3cos (6pi)x ?

  20. ranga
    • one year ago
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    The formula for the period of cos(bx) is: Period = 2pi / b Looking at the graph we found the period to be 6pi. Plug that into the formula: 6pi = 2pi / b Find b.

  21. skullofreak
    • one year ago
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    2pi/6pi = pi/3pi

  22. ranga
    • one year ago
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    The pi will cancel out. so b = ?

  23. skullofreak
    • one year ago
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    yes sorry

  24. skullofreak
    • one year ago
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    1/3

  25. ranga
    • one year ago
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    Yes. Put them all together and the curve represented in the graph is: y = 3cos(1/3*x)

  26. skullofreak
    • one year ago
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    okay thank you!! a lot!

  27. ranga
    • one year ago
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    You are welcome.

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