Consider the following Cone :
Find the Cylindrical and cartesian equation of the above cone.
Answer:
Cylindrical Co-ordinate system:
$ x=r \cos \theta, \\ y=r \sin \theta, \\ z=z , \ \ 0 \leq \theta \leq 2 \pi \ $
Cartesian Co-ordinate system :
$ r=\sqrt{x^2+y^2 } , \\ \theta=\tan^{-1} \frac{y}{x} , \\ z=z \ $
Am I right so far ?
Help me out
In the cylindrical system $z = r$
Then substituting $r = \sqrt {x^2 + y^2}$
Gives $z = \sqrt {x^2+ y^2}$ in Cartesian.