Calculus 3 Problem (explain solution)

[ttran1117]

Homework Statement

Put the equation: p = 2 sin (x) cos (y) into rectangular coordinates. Identify the surface

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

 

[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.

 

[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.

 

[LCKurtz]

Go to http://mathworld.wolfram.com/SphericalCoordinates.html and look at equations 4,5, and 6.

 

[ttran1117]

Oh! I finally get it now lol. thank you