Cylindrical Coordinates

In the cylindrical coordinate system, a point P is represented by a triple $\left(\vphantom{ r,\theta ,z}\right.$r, θ, z$\left.\vphantom{ r,\theta ,z}\right)$, where $\left(\vphantom{ r,\theta }\right.$r, θ$\left.\vphantom{ r,\theta }\right)$ represents a point in polar coordinates and z is the usual rectangular third coordinate. Thus, to convert from cylindrical to rectangular coordinates, we use the equations

x = r cosθ        y = r sinθ        z = z

To go from rectangular to cylindrical coordinates, we use the equations

r2 = x2 + y2        tanθ = $\displaystyle {\dfrac{{y}}{{x}}}$        z = z

The default assumption is that r is a function of θ and z. As usual, you can plot several surfaces on the same axes by dragging expressions onto a plot.



Subsections