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AonZ

  • 2 years ago

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

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  1. dan815
    • 2 years ago
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    |dw:1369436912384:dw|

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

  3. AonZ
    • 2 years ago
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    its sin2A 2sinAcosA

  4. dan815
    • 2 years ago
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    ok

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

  6. AonZ
    • 2 years ago
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    x/3?

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

  8. AonZ
    • 2 years ago
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    the question is x = 3sinA

  9. jdoe0001
    • 2 years ago
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    ok

  10. genius12
    • 2 years 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
    • 2 years ago
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    write the equation simply without A

  12. jdoe0001
    • 2 years ago
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    @genius12 pretty much, is just conversion to rectangular

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

  14. AonZ
    • 2 years ago
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    yes

  15. genius12
    • 2 years 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
    • 2 years ago
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    |dw:1369437576413:dw|

  17. dan815
    • 2 years ago
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    is that readable

  18. jdoe0001
    • 2 years ago
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    |dw:1369437887196:dw|

  19. dan815
    • 2 years ago
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    lol

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

  21. genius12
    • 2 years 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
    • 2 years ago
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    ^ true

  23. jdoe0001
    • 2 years ago
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    right :)

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

  25. dan815
    • 2 years ago
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    |dw:1369437924563:dw|

  26. dan815
    • 2 years ago
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    |dw:1369437958849:dw|

  27. genius12
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    not sure you can get rid of the "x" though, I got the same :S

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

  31. jdoe0001
    • 2 years ago
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    right, so I notice

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

  33. dan815
    • 2 years 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
    • 2 years ago
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    was hard to read dan's writting :P

  35. dan815
    • 2 years ago
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    if u wanna see a nice graph :)

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

  37. AonZ
    • 2 years ago
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    last question :)

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

  39. AonZ
    • 2 years 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
    • 2 years ago
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    |dw:1369438736058:dw|

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

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

  43. dan815
    • 2 years ago
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    |dw:1369439021400:dw|

  44. dan815
    • 2 years ago
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    |dw:1369439046456:dw|

  45. dan815
    • 2 years ago
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    see if that helps

  46. dan815
    • 2 years 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
    • 2 years ago
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    brb

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