Convert cylindrical coordinate displacement to Cartesian

[Madz99]

Summary: I can't figure out how the solver carries out the conversions from cartesian to cylindrical coordinates and vice-versa.

I have a set of points of a finite element mesh which when inputted into a solver (ansys) gives the displacement of each node. I can get the displacement values of each node either in r,theta(in rads),z or x,y,z.
Ex -This is the original coordinates of a node
in cylindrical (r,theta,z) -
0.0480138, 1.634834202, 0.000841226
in Cartesian (x,y,z) -
-0.00307257421, 0.0479153927, 0.000841225971


And the displacement values

in cylindrical -
0.0060519, -0.0054482, 0.0026499
in Cartesian -
0.0050497, 0.0063882, 0.0026499

I can only get the displacement output as either in cylindrical or in cartesian format. Right now I'm taking the output in cylindrical format so I need to calculate x,y displacement values. But I can't figure out how the conversion is performed.
So what I want to know is how the displacement in r,theta,z(0.0060519, -0.0054482, 0.0026499) became x,y,z(0.0050497, 0.0063882, 0.0026499) or vice-versa.
Any help will be appreciated.

[Moderator's note: Moved from a technical forum and thus no template.]

 

[LCKurtz]

Those aren't the correct values for x and y:
> r := 0.60519e-2;
theta := -0.54482e-2;
x := r*cos(theta);
y := r*sin(theta);
print(`output redirected...`); # input placeholder
0.0060519
-0.0054482
0.006051810181
-0.00003297179846