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AonZ

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

  • 11 months ago
  • 11 months ago

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  1. dan815
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    |dw:1369436912384:dw|

    • 11 months ago
  2. dan815
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    is it like that or is it sin^2A

    • 11 months ago
  3. AonZ
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    its sin2A 2sinAcosA

    • 11 months ago
  4. dan815
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    ok

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

    • 11 months ago
  6. AonZ
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    x/3?

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

    • 11 months ago
  8. AonZ
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    the question is x = 3sinA

    • 11 months ago
  9. jdoe0001
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    ok

    • 11 months ago
  10. genius12
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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 months ago
  11. AonZ
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    write the equation simply without A

    • 11 months ago
  12. jdoe0001
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    @genius12 pretty much, is just conversion to rectangular

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

    • 11 months ago
  14. AonZ
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    yes

    • 11 months ago
  15. genius12
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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

    • 11 months ago
  16. dan815
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    |dw:1369437576413:dw|

    • 11 months ago
  17. dan815
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    is that readable

    • 11 months ago
  18. jdoe0001
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    |dw:1369437887196:dw|

    • 11 months ago
  19. dan815
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    lol

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

    • 11 months ago
  21. genius12
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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.

    • 11 months ago
  22. dan815
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    ^ true

    • 11 months ago
  23. jdoe0001
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    right :)

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

    • 11 months ago
  25. dan815
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    |dw:1369437924563:dw|

    • 11 months ago
  26. dan815
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    |dw:1369437958849:dw|

    • 11 months ago
  27. genius12
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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

    • 11 months ago
  28. genius12
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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.

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

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

    • 11 months ago
  31. jdoe0001
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    right, so I notice

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

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

    • 11 months ago
  34. AonZ
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    was hard to read dan's writting :P

    • 11 months ago
  35. dan815
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    if u wanna see a nice graph :)

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

    • 11 months ago
  37. AonZ
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    last question :)

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

    • 11 months ago
  39. AonZ
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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

    • 11 months ago
  40. dan815
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    |dw:1369438736058:dw|

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

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

    • 11 months ago
  43. dan815
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    |dw:1369439021400:dw|

    • 11 months ago
  44. dan815
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    |dw:1369439046456:dw|

    • 11 months ago
  45. dan815
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    see if that helps

    • 11 months ago
  46. dan815
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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

    • 11 months ago
  47. dan815
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    brb

    • 11 months ago
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