Identifying Surfaces in Spherical Coordinates

[josh28]

Homework Statement

$$\rho = sin\theta * sin\phi$$

Homework Equations

I know that $$\rho^{2} = x^{2} + y^{2}+z^{2}$$

The Attempt at a Solution

I tried converting it to cartesian coordinates but I can't seem to get a workable answer that way. I know that the answer is the sphere with radius 1/2 and center (0,1/2,0) but I have no idea how to get there.

Thank you!

 

[Mark44]

Homework Statement

$$\rho = sin\theta * sin\phi$$

Homework Equations

I know that $$\rho^{2} = x^{2} + y^{2}+z^{2}$$

What are the other equations that relate spherical to rectangular coordinates?

The Attempt at a Solution

I tried converting it to cartesian coordinates but I can't seem to get a workable answer that way. I know that the answer is the sphere with radius 1/2 and center (0,1/2,0) but I have no idea how to get there.

Multiply each side of this equation by rho.
$$\rho = sin\theta * sin\phi$$

After that, use the conversion equations to convert everything to rectangular coordinates.

 

[josh28]

Thank you!

 

[Mark44]

Sure - you're welcome!