Express the equation in rectangular coordinates

[Mdhiggenz]

Homework Statement

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.

The answer is x²-y²=z

Guidance is appreciated (:

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

An equation is given in spherical coordinates. Express the equation in rectangular coordinates.

r²cos2∅=z

So first thing I did was used a [STRIKE]half[/STRIKE] double angle formula

r² (cos²∅-sin²∅)=z

Now, I'm stuck.

The answer is x²-y²=z

Guidance is appreciated (:

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.)

 

[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?

 

[gabbagabbahey]

Homework Statement

An equation is given in spherical coordinates. Express the equation in rectangular coordinates.

r²cos2∅=z

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?

So first thing I did was used a half angle formula

r² (cos²∅-sin²∅=z

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