# Math Help - parametrization of a cone

1. ## 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!

2. ## One way to do it

Given your angle $\phi$, you have
$
tan \phi = r/z
$

giving

$
r ^ 2 = z ^ 2 tan ^2 \phi
$

$
x ^ 2 +y^ 2= z ^ 2 tan ^2 \phi
$