Question

Are the two polar coordinates the same: (8, 10pi), (-8, 10pi)?

Answer 1

No

Explanation:

The negative value on one radius (and not on the other) indicates that the distance is to be measured in the opposite direction from the origin.

In this particular case we could note that `10pi` is equivalent to an angle of `0`.
Viewed using Cartesian axis, the polar coordinate: `(8,10pi)` would be a distance of `8` along the X-axis to the right of the origin.
and
the polar coordinate: `(-8,10pi)` would be a distance of "8# along the X-axis to the left of the origin.