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Math Help - Polar and Rectangular coordinates

  1. #1
    stryker213
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    Polar and Rectangular coordinates

    need help with these two problems:

    1. For a give rectangle coordinate, find two pairs of polar coordinates for the poing. One pair satisfies r≥0 and 0≤theta<2pi, and the second pair satisies r≥0 and -2pi<theta≤0
    for the problem (-3, 3sqrt(3))

    2. Identify the curve by transforming Rsin(theta)=4 into rectangular coordinates.
    So far, I converted it to 4csc(theta) but now i'm stuck.
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  2. #2
    Super Member

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    Hello, stryker213!

    1. For a given rectangle coordinates, find two pairs of polar coordinates for the point.
    One pair satisfies r > 0 and 0 ≤ θ < 2π,
    and the second pair satisfies r ≥ 0 and -2π < θ ≤ 0
    for the problem (-3, 3√3)
    We are given: .x = -3, .y = 3√3. .The point is in Quadrant 2.
    . . . . . . . . . .____________
    Then: .r .= .√(-3)² + (3√3)² .= .6

    And: .tanθ .= .(3√3)/(-3) .= .-√3 . . θ = 2π/3


    The polar coordinates are: .(6, 2π/3) and (6, -4π/3)



    2. Identify the curve by transforming r·sinθ = 4 into rectangular coordinates.
    You're expected to know the conversion formulas: .x .= .r·cosθ, .y .= .r·sinθ

    Then .r·sinθ = 4 .becomes .y = 4, a horizontal line.

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