Cylindrical coordinate convertion

[alexmolinavr6]

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

 

[Mark44]

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

 

[alexmolinavr6]

yes but I need to find
x
y
z
r
Ɵ
ρ
ɸ

 

[Mark44]

What does the equation r sinƟ = 2 represent geometrically?

 

[alexmolinavr6]

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

 

[alexmolinavr6]

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

 

[Mark44]

What can you replace rsinƟ with? BTW your conversion formulas from cylindrical to rectangular are wrong.

 

[alexmolinavr6]

From Cyl to rectangle
x=cosƟ y=sinƟ z=z

ok
x=rcosƟ y=rsinƟ

 

[alexmolinavr6]

What can you replace rsinƟ with? BTW your conversion formulas from cylindrical to rectangular are wrong.

y=2
ok, I'm getting somewhere

 

[Mark44]

Yes, you have now partially answered my question in post 4. What does y = 2 represent geometrically?