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22 March, 20:08

Write the equation in spherical coordinates. (a) 4z2 = 5x2 + 5y2 (b) x2 + 3z2 = 4

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Answers (2)
  1. 22 March, 20:18
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    (753,#53) Write the equation A) in cylindrical coordinates B) spherical coordinates. Solution: A) in cylindrical coordinates, B) in spherical coordinates,
  2. 22 March, 20:32
    0
    Refer to the diagram shown below.

    The transformation from the Cartesian coordinate system (x, y, z) to the spherical coordinate system (r,θ,φ) is given by

    x = rsinφcosθ

    y = rsinφsinθ

    z = rcosφ

    Part a.

    The given equation is 4z² = 5x² + 5y².

    In spherical coordinates, obtain

    4r²cos²φ = 5r²sin²φ cos²θ + 5r²sin²φ sin²θ

    = 5r²sin²φ (cos²θ + sin²θ)

    = 5r²sin²φ

    4/5 = tan²φ

    tanφ = 2/√5 = (2/5) √5

    Answer: tanφ = (2/5) √5

    Part b.

    The given equation is x² + 3z² = 4

    In spherical coordinates, obtain

    r²sin²φ cos²θ + 3r²cos²φ = 4

    Answer: r² (sin²φ cos²θ + 3cos²φ) = 4
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