Question

What are the polar coordinates of (0,-sqrt10)

Answer 1

As the x coordinate is 0, we see it lies on the (negative) y axis, and so theta is 3pi/2
the radius is the square root of the sum of the squares of x and y, so
\[r = \sqrt{0^2 + (-\sqrt{10})^2} = \sqrt{10}\]

Answer 2

The x coordinate was sqrt10 but it doesn't accept theta as 3pi/2

Answer 3

does it have to be in the interval (-pi, pi) ? Then subtract 2pi from it:
-pi/2 is the same angle.