Describe the surface in cylindrical coordinates?

[Colts]

Homework Statement

The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z)

Homework Equations

No clue

The Attempt at a Solution

No clue

 

[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.

 

[Colts]

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

 

[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

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

 

[LCKurtz]

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

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

 

[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

 

[LCKurtz]

in this case theta is the angle [itex]\phi [/phi] in the equations above

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

 

[Colts]

Got it. Thanks guys