Math - Metric for Spherical Coords

Compute Covariant and Contravariant Metric Tensor for Spherical Coordinates

Where:  e1, e2, e3  are a covariant basis. 

Now Compute the Contravariant Metric Tensor

Where   e^1, e^2, e^3   are a contravariant basis.

Below is another way to compute ds*ds wihtout computing the metric 

Compute dx, dy, and dz

Expand the squared terms

Combine terms and use trig identity  cos^2 +sin^2 = 1