# Cylindrical coordinates

1. Apr 25, 2007

### seang

1. The problem statement, all variables and given/known data

Say I have line, y = - 5 in cartesian coordinates. How do I express this in cylindrical coordinates?

Also, if I have a point (0,-5) in cartesian coordinates, how to I express this position vector in cylindrical coordinates?

2. Relevant equations

y = r sin (phi)

j = r(hat)cos (phi) - phi(hat) sin (phi)

3. The attempt at a solution

THe relations are right there but I've forgotten howto use them.

2. Apr 25, 2007

### mjsd

do you remember how to turn say $$(x,y)$$ into $$(r,\theta)$$ in 2D? the idea there is similar...

3. Apr 26, 2007

### HallsofIvy

Staff Emeritus
Cylindrical coordinates? That's in 3d but you only mention 2 coordinates? Perhaps you mean polar coordinates- cylindrical coordinates but ignore the z component.

You mention $y= r sin(\phi)$ (I would have used $\theta$). Do you also know that $x= r cos(\phi)$? Solve those two equations for r and $\phi$ in terms of x and y. The first is easy! You can eliminate $\phi$ by squaring both equations and adding. The second is about as easy: eliminate r by dividing one equation by the other.