Question

Are the two polar coordinates the same: (0, 8pi), (0, 9pi/4)?

Answer 1

Yes. See explanation.

Explanation:

If the radius is zero, then for every angle `varphi` the polar coordinates represent point `(0,0)`. This can be easily seen if you look at the formulas changing polar coordinates to Cartesian coordinates:

`{(x=rcosvarphi),(y=rsinvarphi):}`

If `r=0` then for every angle the cartesian coordinates will be `(0,0)`