Solutions to Cylindrical Coordinates Exercises

1. The set of all points with r = 5 looks like an infinite cylinder with radius 5 about the z-axis.
2. The set of all points with theta = pi / 5 looks like a half-plane orthogonal to the xy-plane and having the z-axis as its boundary.
3. A plane looks like A r cos theta + B r sin theta + C z + D = 0. A line looks like ...
   The other two variables in cylindrical-x should be called theta and x, with theta = tan^-1 (z/y) and x = x providing the conversions to cartesian coordinates.
   The point with cartesian coordinates (1,2,3) is (r = sqrt(14), theta = tan^-1(2), z = 3) in cylindrical coordinates.
   The point with cylindrical coordinates (r = 2, theta = pi, z = 5) is ( -2, 0, 5) in cartesian coordinates.