Question

What is the polar form of `(1,3)`?

Answer 1

`(r,theta)=(sqrt(10),arctan(3)) approx (3.16,1.25)`, where the second number is measured in radians.

Explanation:

The polar coordinates `(r,theta)` of a point with rectangular coordinates `(x,y)` satisfy `r^{2}=x^{2}+y^{2}` and `tan(theta)=y/x` (when `x !=0`). Since the point `(x,y)=(1,3)` is in the first quadrant, we can use the arctangent function to solve for the angle if we take `r` to be the positive square root of `x^{2}+y^{2}=1^{2}+3^{2}=10`.