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skullofreak

  • 2 years ago

help!!

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

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

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

  5. skullofreak
    • 2 years 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
    • 2 years ago
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    So what is the difference between this one and cosx?

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

  8. skullofreak
    • 2 years ago
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    nvm its cos

  9. ranga
    • 2 years 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
    • 2 years ago
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    a = 3

  11. skullofreak
    • 2 years ago
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    so y = 3cos.. bx

  12. ranga
    • 2 years 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
    • 2 years ago
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    every 3pi?

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

  15. ranga
    • 2 years 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
    • 2 years ago
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    6pi/2

  17. ranga
    • 2 years 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
    • 2 years ago
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    OH

  19. skullofreak
    • 2 years ago
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    y=3cos (6pi)x ?

  20. ranga
    • 2 years 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
    • 2 years ago
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    2pi/6pi = pi/3pi

  22. ranga
    • 2 years ago
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    The pi will cancel out. so b = ?

  23. skullofreak
    • 2 years ago
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    yes sorry

  24. skullofreak
    • 2 years ago
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    1/3

  25. ranga
    • 2 years 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
    • 2 years ago
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    okay thank you!! a lot!

  27. ranga
    • 2 years ago
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    You are welcome.

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