# Express the equation in rectangular coordinates

1. Oct 5, 2012

### Mdhiggenz

1. The problem statement, all variables and given/known data
An equation is given in spherical coordinates. Express the equation in rectangular coordinates.

r2cos2∅=z

So first thing I did was used a half angle formula

r2 (cos2∅-sin2∅=z

Now, i'm stuck.

Guidance is appreciated (:

2. Relevant equations

3. The attempt at a solution

2. Oct 5, 2012

### SammyS

Staff Emeritus
That looks fine.

(You might like to use a symbol such as theta, θ, for an angle rather than the symbol used for the null set, ∅ . I don't know why phi, ϕ, is not include in the symbol box.)

3. Oct 5, 2012

### Mdhiggenz

Thanks for the response and sorry for the minor errors, I'm still a bit confused on how I can manipulate what I have to make it to look more like x^2-y^2=z.

What i'm thinking is if I just distribute the r^2. I will get (r^2cosθ^2)-(r^2sinθ^2)=z

and if rcosθ=x and rsinθ =y

then these are just the same values but squared. Which would give me X^2-y^2=z.

Would that be a correct assumption?

4. Oct 5, 2012

### gabbagabbahey

I assume that ∅ is meant to be $\phi$?

There are 2 common conventions for spherical coordinates $(r, \theta, \phi)$. In one convetion,$\theta$ is the polar angle and $\phi$ is the azimuthal angle[/itex], and vice versa in the other convention. Which convention are you using?

What are $x$, $y$, and $z$ in terms of spherical coordinates? What is $x^2-y^2$?