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Math Help - parametrization of a cone

  1. #1
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    Exclamation parametrization of a cone

    how would i parameterize a cone if i am given phi=a constant
    for example, phi=pi/3

    i know that phi is the angle created from the line from the origin..but how would i illustrate/parameterize when given a constant for phi?

    thanks i have an exam tomorrow so i'm trying to study and figure everything out!
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  2. #2
    Senior Member
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    One way to do it

    Given your angle \phi, you have
    <br />
tan \phi = r/z<br />

    giving

    <br />
r ^ 2 = z ^ 2 tan ^2 \phi<br />

    <br />
x ^ 2 +y^ 2= z ^ 2 tan ^2 \phi<br />
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