Solving cylindrical coordinates system, just want to check my answer

[jhosamelly]

Homework Statement

.. Here is the question;

In cylindrical coordinate system ,
(a) If r = 2 meters , $\varphi$ = 35° , z = 1 meter , what are x,y,z?
(b) if (x,y,z) = (3,2,4) meters, what are (r, $\varphi$, z)

Homework Equations

x = r cos $\varphi$
y = r sin $\varphi$
z = z

r = $\sqrt{(x)^{2}+(y)^{2}}$
$\varphi$= $tan^{-1}$ $\frac{y}{x}$
z=z

The Attempt at a Solution

here is my answer, i just want to know if I'm correct

for a.

x = r cos $\varphi$
= 2 cos 35
= 1.64

y = r sin $\varphi$
= 2 sin 35°
= 1.15

z = z
z = 1


for b.


r = $\sqrt{(x)^{2}+(y)^{2}}$
= $\sqrt{(3)^{2}+(2)^{2}}$
= 3.6 ≈ 4


$\varphi$= $tan^{-1}$ $\frac{y}{x}$
= $tan^{-1}$ $\frac{2}{3}$
= 33.69° ≈ 34°

z = z
z = 4

 

[zjgarvey1]

Yep, looks good. If you want to check yourself, you can always draw it out in both coordinate systems (they should be close to the same place if the graphs are drawn hastily).

 

[jhosamelly]

thanks.. I was just confused because the other books I saw use $\rho$ instead of r.. i thought i still need to do something to r to make it $\rho$ .. hehe.. Thanks. )

 

[zjgarvey1]

I always used ρ for spherical coordinates and r for the xy-plane. But as long as your equations are consistent with what you are trying to do, it doesn't matter if you draw a little duckie as a variable.