Rectangular to Spherical Coordinate conversion....

[Unicow]

Homework Statement

Convert from rectangular to spherical coordinates.
(-(sqrt3)/2 , 3/2 , 1)

Homework Equations

We know the given equations are
ρ = sqrt(x^2 + y^2 + z^2)
tan theta = y/x
cos φ = z / ρ

The Attempt at a Solution

My answer was (2, -pi/3, pi/3)
It should be a simple plug and go... Am I doing simple math wrong? The only part I think I could get wrong is the y/x but -3 / 2 / sqrt3 / 2 should be sqrt3 right?I'm using webassign if that matters at all. I'm sorry for posting such a simple question but I don't understand how that solution is wrong... I guess I'm just having a huge brain fart?

 

[Mark44]

Homework Statement

Convert from rectangular to spherical coordinates.
(-(sqrt3)/2 , 3/2 , 1)

Homework Equations

We know the given equations are
ρ = sqrt(x^2 + y^2 + z^2)
tan theta = y/x
cos φ = z / ρ

The Attempt at a Solution

My answer was (2, -pi/3, pi/3)
It should be a simple plug and go... Am I doing simple math wrong? The only part I think I could get wrong is the y/x but 3 / 2 / sqrt3 / 2 should be sqrt3 right?

No, since $x = \frac{-\sqrt 3}{2}$. You are ignoring the sign, so your value for $\theta$ will be wrong.

I'm using webassign if that matters at all. I'm sorry for posting such a simple question but I don't understand how that solution is wrong... I guess I'm just having a huge brain fart?

 

[Unicow]

No, since $x = \frac{-\sqrt 3}{2}$. You are ignoring the sign, so your value for $\theta$ will be wrong.

Sorry I must have deleted the negative sign by accident while I was editing. I've edited it back in and I had counted that into my calculations and that's why my theta is negative pi / 3 instead of positive.

 

[Mark44]

Your answer of (2, -pi/3, pi/3) looks fine to me. Is it possible that WebAssign doesn't recognize "pi" and wants you to enter a decimal value?
Sometimes these programs are brain-dead...

 

[Unicow]

Your answer of (2, -pi/3, pi/3) looks fine to me. Is it possible that WebAssign doesn't recognize "pi" and wants you to enter a decimal value?
Sometimes these programs are brain-dead...

Yeah it's really frustrating especially considering it's such an easy question. I've tried decimal already and the simple "pi" or whatever, is correct for all the other choices...

 

[Mark44]

Homework Equations

We know the given equations are
ρ = sqrt(x^2 + y^2 + z^2)
tan theta = y/x
cos φ = z / ρ

The second and third equations above are wrong, according to this wiki article (https://en.wikipedia.org/wiki/Spherical_coordinate_system).
$\theta = \arccos(z/r)$ Here r is the same as your $\rho$.
$\phi = \arctan(y/x)$

 

[Unicow]

The second and third equations above are wrong, according to this wiki article (https://en.wikipedia.org/wiki/Spherical_coordinate_system).
$\theta = \arccos(z/r)$ Here r is the same as your $\rho$.
$\phi = \arctan(y/x)$

There's no way that can be right... I've already done a few questions and gotten them all right except for this one... Also, I might trust the textbook more than wikipedia. I hope you don't take this as an insult or anything because I do appreciate the help.

 

[Mark44]

There's no way that can be right... I've already done a few questions and gotten them all right except for this one... Also, I might trust the textbook more than wikipedia. I hope you don't take this as an insult or anything because I do appreciate the help.

No, I don't take it as an insult at all. The wiki formulas seem weird to me, as well, and that's why I qualified my answer.

I checked with wolframalpha, which gives an answer of (2, pi/3, 2pi/3) -- http://www.wolframalpha.com/input/?i=spherical+coordinates(-sqrt(3)/2,+3/2,+1).
Not all books use the notation in the same way. For a point $(\rho, \theta, \phi)$, some books call $\theta$ the inclination (measured away from the z-axis), and others call $\phi$ the inclination. These differences make your formulas correct as far as some books are concerned and incorrect in others.

 

[Unicow]

No, I don't take it as an insult at all. The wiki formulas seem weird to me, as well, and that's why I qualified my answer.

I checked with wolframalpha, which gives an answer of (2, pi/3, 2pi/3) -- http://www.wolframalpha.com/input/?i=spherical+coordinates(-sqrt(3)/2,+3/2,+1).
Not all books use the notation in the same way. For a point $(\rho, \theta, \phi)$, some books call $\theta$ the inclination (measured away from the z-axis), and others call $\phi$ the inclination. These differences make your formulas correct as far as some books are concerned and incorrect in others.

Ahh I see and understand now haha. Thank you for your help and it completely went over my head about how it could be more than one value of "n * pi / 3" for theta to be the value. I got the correct answer! Thank you so so much.

 

[Orodruin]

The typical convention in physics is that $\theta$ is the polar angle and $\varphi$ the azimuthal angle. In mathematics, the convention is usually the other way around. The Wikipedia page shows both conventions.