Converting multidimensional polar coordinates to cartesian?

Question

Hi all,

I'm given a set of multidimensional polar coordinates: (R,Theta_1,....Theta_n-1)

I need to know how to convert it to cartesian coordinates:
(X_1,X_2,...,X_n)

Thanks!

Answer 1

If theta_1 is the angle the radius vector makes with the x_1 axis, and theta_2 is.....etc., then

x1= R cos theta_1
x2= R cos theta_2
.
.
.
x_n-1=R cos theta_(n-1)

and while there is probably some really elegant way to get the remaining coordinate, all I can think of at the moment is to use the fact that the sum of the squares of the n coordinates equals R^2, and solve for x_n.