Cylindrical coordinate convertion

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Homework Help Overview

The discussion revolves around converting cylindrical coordinates, specifically the equation r=2cscƟ, into both rectangular and spherical coordinates. Participants are exploring the relationships between these coordinate systems and the implications of the given equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express the cylindrical coordinates in rectangular and spherical forms, with some focusing on the geometric interpretation of the equation r sinƟ = 2. Questions about the correctness of conversion formulas and the implications of the derived equations are also raised.

Discussion Status

Some participants have made progress in expressing relationships between the coordinates, particularly noting that y=2 is a significant finding. However, there is still uncertainty regarding the geometric meaning of the equations and the accuracy of the conversion methods being discussed.

Contextual Notes

There are indications of confusion regarding the conversion formulas from cylindrical to rectangular coordinates, with participants questioning their validity. Additionally, the original poster expresses difficulty in progressing beyond certain points in the conversion process.

alexmolinavr6
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Homework Statement


cylindrical coordinates: r=2cscƟ, give both rectangular and spherical cordinates



Homework Equations


I know this:
From rectangular to cylinder
z=z r2=x2+y2 tanƟ=y/x
From Cyl to rectangle
x=cosƟ y=sinƟ z=z
From cyl to spherical
Ɵ=Ɵ ρ2=x2+y2+z2 ɸ=sin-1r/ρ
From Spherical to cylindrical
Ɵ=Ɵ r=ρsinɸ z=ρcosɸ



The Attempt at a Solution


so far what I have is
r=2/sinƟ



can anyone please help me, I got stuck
 
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alexmolinavr6 said:

Homework Statement


cylindrical coordinates: r=2cscƟ, give both rectangular and spherical cordinates



Homework Equations


I know this:
From rectangular to cylinder
z=z r2=x2+y2 tanƟ=y/x
From Cyl to rectangle
x=cosƟ y=sinƟ z=z
From cyl to spherical
Ɵ=Ɵ ρ2=x2+y2+z2 ɸ=sin-1r/ρ
From Spherical to cylindrical
Ɵ=Ɵ r=ρsinɸ z=ρcosɸ



The Attempt at a Solution


so far what I have is
r=2/sinƟ



can anyone please help me, I got stuck
So r sinƟ = 2
 
yes but I need to find
x
y
z
r
Ɵ
ρ
ɸ
 
What does the equation r sinƟ = 2 represent geometrically?
 
Mark44 said:
What does the equation r sinƟ = 2 represent geometrically?

im not sure, what i know is that 1/sinƟ = cscƟ. and since in the conversions i have "sin"
thats why I replaced r=2cscƟ with r=2/sinƟ
someone elso solved for 2 and got rsinƟ=2
 
Mark44 said:
What does the equation r sinƟ = 2 represent geometrically?

im not sure, what i know is that 1/sinƟ = cscƟ. and since in the conversions i have "sin"
thats why I replaced r=2cscƟ with r=2/sinƟ
someone else solved for 2 and got rsinƟ=2
 
What can you replace rsinƟ with? BTW your conversion formulas from cylindrical to rectangular are wrong.
 
alexmolinavr6 said:
From Cyl to rectangle
x=cosƟ y=sinƟ z=z

ok
x=rcosƟ y=rsinƟ
 
Mark44 said:
What can you replace rsinƟ with? BTW your conversion formulas from cylindrical to rectangular are wrong.

y=2
ok, I'm getting somewhere
 
Last edited:
  • #10
Yes, you have now partially answered my question in post 4. What does y = 2 represent geometrically?
 

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