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Math Help - How do i solve this trig problem - Polar equations.

  1. #1
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    How do i solve this trig problem - Polar equations.

    Here is the problem that I cannot figure out how to do. Please explain.

    r = (5csc(θ))/(6csc(θ) + 3)
    possibilities:
    a) (36x^2) + (27y^2) + (30x) -25 = 0
    b) (27x^2) + (36y^2) +(30x) -25 = 0
    c) (36x^2) + (27y^2) + (30y) -25 = 0
    d) none of the above

    Thankyou so much for any help
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jackschmerold View Post
    Here is the problem that I cannot figure out how to do. Please explain.

    r = (5csc(θ))/(6csc(θ) + 3)
    possibilities:
    a) (36x^2) + (27y^2) + (30x) -25 = 0
    b) (27x^2) + (36y^2) +(30x) -25 = 0
    c) (36x^2) + (27y^2) + (30y) -25 = 0
    d) none of the above

    Thankyou so much for any help
    What have you done so far? (Is this from a homework assignment by any chance?)
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  3. #3
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    Yes it is a hw problem.
    So far:
    6rcsc(θ) + 3r = 5cscθ
    3r = 5cscθ - 6rcscθ
    (3r)^2 = (5cscθ)^2 - (6rcscθ)^2
    3x^2 + 3y^2 = ?
    I dont know where to go from there
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jackschmerold View Post
    Yes it is a hw problem.
    So far:
    6rcsc(θ) + 3r = 5cscθ
    3r = 5cscθ - 6rcscθ
    (3r)^2 = (5cscθ)^2 - (6rcscθ)^2
    3x^2 + 3y^2 = ?
    I dont know where to go from there
    Here's a suggestion. When you're here: 6r\csc\theta+3r=5\csc\theta, multiply both sides by \sin\theta to get 6r+3r\sin\theta=5.

    Now make the conversion to rectangular coordinates. Can you take from here?
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jackschmerold View Post
    Yes it is a hw problem.
    So far:
    6rcsc(θ) + 3r = 5cscθ
    3r = 5cscθ - 6rcscθ
    (3r)^2 = (5cscθ)^2 - (6rcscθ)^2
    3x^2 + 3y^2 = ?
    I dont know where to go from there
    Here's a suggestion. When you're here: 6r\csc\theta+3r=5\csc\theta, multiply both sides by \sin\theta to get 6r+3r\sin\theta=5.

    Now make the conversion to rectangular coordinates. Can you take from here?
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