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    Cylindrical and spherical coordinates.

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    Write the equations

    i) x^2 - y^2 - 2z^2 = 4 and

    ii) z = x^2 - y^2 in

    a) cylindrical coordinates
    b) spherical coordinates

    give detailed explanation for each step of the solutions.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:44 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/cylindrical-and-spherical-coordinates-8729

    Solution Preview

    i.)
    a.)
    phi == p = angle in x-y plane with respect to X-Z plane
    x = r*cos(p)
    y = r*sin(p)
    z = z
    substitute the values in x^2 - y^2 - 2z^2 = 4
    => r^2 * cos^2(p) - r^2 * sin^2(p) - 2z^2 = 4
    => r^2 * cos(2*p) - 2z^2 = 4 ...

    Solution Summary

    Cylindrical and spherical coordinates are determined.

    $2.49

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