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AonZ

  • one year ago

Eliminate A from each pair of parametric equations x = 3sinA y= 6sin2A

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  1. dan815
    • one year ago
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    |dw:1369436912384:dw|

  2. dan815
    • one year ago
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    is it like that or is it sin^2A

  3. AonZ
    • one year ago
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    its sin2A 2sinAcosA

  4. dan815
    • one year ago
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    ok

  5. jdoe0001
    • one year ago
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    from x= 3sin(a), what would sin(a) be?

  6. AonZ
    • one year ago
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    x/3?

  7. jdoe0001
    • one year ago
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    .. right... ... is x= 3sin(a), what you have or x = 3cos(a)?

  8. AonZ
    • one year ago
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    the question is x = 3sinA

  9. jdoe0001
    • one year ago
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    ok

  10. genius12
    • one year ago
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    Btw, what do you mean by eliminate? Are you to convert this in to a rectangular equation with y in terms of x or are you to have both x and y written in terms of something else that isn't A? @AonZ

  11. AonZ
    • one year ago
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    write the equation simply without A

  12. jdoe0001
    • one year ago
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    @genius12 pretty much, is just conversion to rectangular

  13. genius12
    • one year ago
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    So y in terms of x and not A right?

  14. AonZ
    • one year ago
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    yes

  15. genius12
    • one year ago
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    \[\bf x=3\sin(A) \implies \frac{x}{3}=\sin(A) \implies \sin^{-1} \left( \frac{x}{3}\right)=A\]Plug this value of A in y = 6sin(2A) and you're done. @AonZ

  16. dan815
    • one year ago
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    |dw:1369437576413:dw|

  17. dan815
    • one year ago
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    is that readable

  18. jdoe0001
    • one year ago
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    |dw:1369437887196:dw|

  19. dan815
    • one year ago
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    lol

  20. dan815
    • one year ago
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    well he shudnt get the asnwer too easily so its all good :)

  21. genius12
    • one year ago
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    Both @dan815 and mine rectangular forms work. Except his makes it more obvious that cosine and sine can be used parametrically to give an ellipse as dan's rectangular form is the equation of an ellipse.

  22. dan815
    • one year ago
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    ^ true

  23. jdoe0001
    • one year ago
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    right :)

  24. AonZ
    • one year ago
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    |dw:1369437893899:dw| i dont it get when u went into that part

  25. dan815
    • one year ago
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    |dw:1369437924563:dw|

  26. dan815
    • one year ago
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    |dw:1369437958849:dw|

  27. genius12
    • one year ago
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    Rearrange x and y so that:\[\bf \frac{y}{4x}=\cos(A) \ and \ \frac{x}{3}=\sin(A)\]Squaring both sides of both equations gives:\[\bf \left( \frac{y}{4x} \right)^2=\cos^2(A) \ and \ \left( \frac{x}{3} \right)^2=\sin^2(A)\]Adding both equations and using the identity cos^2(A) + sin^2(A) = 1 gives u the rectangular form. @AonZ

  28. genius12
    • one year ago
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    I just realised, @dan815 rectangular form actually won't be an ellipse even thought i looks like it will be lol. There is an x in the denominator under y which means it can't be the equation of an ellipse.

  29. jdoe0001
    • one year ago
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    not sure you can get rid of the "x" though, I got the same :S

  30. dan815
    • one year ago
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    u dont need to they just want an equation without A

  31. jdoe0001
    • one year ago
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    right, so I notice

  32. AonZ
    • one year ago
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    thank you so much :D understood @genius12 way much better

  33. dan815
    • one year ago
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    http://www.wolframalpha.com/input/?i=%28y%2F%284x%29%29%5E2%2B%28x%2F3%29%5E2%3D1

  34. AonZ
    • one year ago
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    was hard to read dan's writting :P

  35. dan815
    • one year ago
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    if u wanna see a nice graph :)

  36. AonZ
    • one year ago
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    can i pls get help on 1 more question? http://openstudy.com/study#/updates/519ff981e4b04449b221f091

  37. AonZ
    • one year ago
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    last question :)

  38. jdoe0001
    • one year ago
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    just post in the channel, so we can all see it and thus help :)

  39. AonZ
    • one year ago
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    got a link :P http://openstudy.com/study#/updates/519ff981e4b04449b221f091 but Question is Eliminate A from each pair of parametric equations x = 2tan( A/2) y = cosA

  40. dan815
    • one year ago
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    |dw:1369438736058:dw|

  41. dan815
    • one year ago
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    2 ways to go from cosa to a/2 or other way, which trig u know

  42. dan815
    • one year ago
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    theres also an identity u can use straight from tan to a double angle

  43. dan815
    • one year ago
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    |dw:1369439021400:dw|

  44. dan815
    • one year ago
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    |dw:1369439046456:dw|

  45. dan815
    • one year ago
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    see if that helps

  46. dan815
    • one year ago
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    look at the formula for Cos(2a) and that tan^2a either one of those will help you simplify and eliminate a

  47. dan815
    • one year ago
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    brb

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