Question

How do you convert (0, 9) into polar coordinates?

Answer 1

It turns out that when the argument for the arctangent is undefined, this means that the angle is either `90` degrees or `270` degrees. Because the y coordinate is positive, this means that the angle theta is `90` degrees.

The radius is `r=sqrt(x^2+y^2)=sqrt(0^2+9^2)=9`

Hence the point `(0,9)` in polar coordinates is `(9,90^o)`.

Remember that when you have a point in cartesian cooridnates
`(x,y)` its polar coordinates are

`(sqrt(x^2+y^2),arctan(y/x))`