# Homework Help: Converting Spherical to Cartesian

1. Mar 1, 2010

### bglb212

Problem solved!

Last edited: Mar 1, 2010
2. Mar 1, 2010

### Staff: Mentor

Your equation is equivalent to $\rho$ = cos($\phi$)/(1 - cos2($\phi$).

Your relevant equations show the converstion from spherical to Cartesian coordinates. Do you know the conversions going in the other direction?

One trick that will be helpful is to multiply both sides by rho. This potentially adds a point (rho = 0) that might not be a solution of your original equation, so you should check whether this is already a solution of your equation.

3. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
4. Mar 1, 2010

### Staff: Mentor

As an intermediate step, look at what I have in my previous post. Use trig identities to get to what I showed, then go from there.

5. Mar 1, 2010

### vela

Staff Emeritus
Look at the equations for x, y, and z. Note that they're all of the form rho times some combination of sines and cosines. So the first thing you should do is rewrite everything in terms of sines and cosines. Next, rearrange terms so the trig functions multiply rho. If needed, do as Mark suggested, and multiply both sides by rho. Then try to identify what cartesian coordinates the various products are equal to.

6. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
7. Mar 1, 2010

### Staff: Mentor

You're missing a factor of cos(phi) in the numerator on the right side.

8. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
9. Mar 1, 2010

### vela

Staff Emeritus
Try bringing the (1+cos^2(phi)) to the other side.

10. Mar 1, 2010

### Staff: Mentor

OK. I didn't catch what you were doing.

Don't you mean (1 - cos^2(phi))?

11. Mar 1, 2010

### Staff: Mentor

It's probably helpful not to change the rho^2 on the left side just yet.

12. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
13. Mar 1, 2010

### Staff: Mentor

Let us decide whether nothing good comes out of it. Show us what you tried.

You have rho^2 = z/(1 - cos^2(phi))
What do you get when you multiply both sides by 1 - cos^2(phi)?

14. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
15. Mar 1, 2010

### vela

Staff Emeritus
Yes, I did. Thanks for catching that.

16. Mar 1, 2010

### Staff: Mentor

That's a very nice thing to say! Thank you!

17. Mar 1, 2010

### bglb212

Solved!

Last edited: Mar 1, 2010
18. Mar 1, 2010

### Staff: Mentor

csc(x) = 1/sin(x), cot(x) = cos(x)/sin(x)

Are those the ones you mean?

19. Mar 1, 2010

### Staff: Mentor

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