# Homework Help: Describe the surface in cylindrical coordinates?

1. Sep 16, 2012

### Colts

1. The problem statement, all variables and given/known data
The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z)

2. Relevant equations
No clue

3. The attempt at a solution
No clue

2. Sep 16, 2012

### damabo

in your book, you will probably find equations for x, for y in terms of theta and z. don't have my book here with me.

3. Sep 16, 2012

### Colts

I don't understand what r=f(theta,z) means and how to write my answer in that form

4. Sep 16, 2012

### damabo

apparently, this is the conversion from cartesian coordinates (x,y,z) to cilindrical (rho, phi, z):

$x = \rho \cos \varphi$
$y = \rho \sin \varphi$

$\rho = \sqrt{x^{2}+y^{2}}$ and

$\varphi = \begin{cases} 0 & \mbox{if } x = 0 \mbox{ and } y = 0\\ \arcsin(\frac{y}{\rho}) & \mbox{if } x \geq 0 \\ -\arcsin(\frac{y}{\rho}) + \pi & \mbox{if } x < 0\\ \end{cases}$

5. Sep 16, 2012

### LCKurtz

Substitute $x=r\cos\theta,\, y=r\sin\theta$ in the equation and solve it for $r$.

6. Sep 16, 2012

### damabo

f(theta, z) means that you should equate radius to a function of theta and z. in this case theta is the angle [itex]\phi [/phi] in the equations above. this angle, simply put, is the same as the angle in polar coordinates. the only difference between polar coordinates and cilindrical, is that with cilindrical, you have height (z) as well

7. Sep 16, 2012

### LCKurtz

$\theta$ is given by \theta, not \phi.

8. Sep 16, 2012

### Colts

Got it. Thanks guys