Calculus 3 Problem (explain solution)

1. Oct 18, 2009

ttran1117

1. The problem statement, all variables and given/known data
Put the equation: p = 2 sin (x) cos (y) into rectangular coordinates. Identify the surface

3. The attempt at a solution
I tried to look at all the identities but I can't seem to figure out which one to use. I have the solutions to this problem, which follows:

p^2 = 2 p sin x cos y
=> x^2 + y^2 + z^2 = 2x (Where did this come from?)
=> x^2 - 2x + y^2 + z^2 = 0
=> (x^2-2x+1) + y^2 + z^2 = 1, which is a sphere of axis (1,0,0)

Can anyone explain the solution? Thank you

2. Oct 18, 2009

LCKurtz

Apparently you are dealing with spherical coordinates and the variable you are calling p is actually the spherical coordinate usually denoted as $\rho$. And, what's worse, the x and y in your equation also don't represent the cartesian x and y. Here's what I think your given equation should be:

$$\rho = 2\sin(\phi)cos(\theta)$$

where $(\rho,\phi, \theta)$ are the spherical coordinates of (x,y,z). Try following your argument knowing that and using the usual spherical coordinate formulas.

3. Oct 18, 2009

ttran1117

You're right. That is supposed to be the right equation, but I just used x and y because I didn't understand how to use the symbols lol. I was/am browsing through my textbook and notes, but was unable to find to relate rho, phi, and theta to spherical coordinates. I understand that x^2 + y^2 and z^2 is the spherical formula, but I still don't understand the 2x portion.

4. Oct 18, 2009

LCKurtz

5. Oct 18, 2009

ttran1117

Oh! I finally get it now lol. thank you