What is (2,9) in polar coordinates?

1 Answer
Dec 3, 2015

(r,θ)=(85,arctan(92)+π)(9.22,1.79), where the 1.79 is the angle measure in radians.

Explanation:

The polar coordinates (r,θ) of a point in the plane are related to the rectangular coordinates of the point by the equations r2=x2+y2 and tan(θ)=yx (when x0).

Since the point whose rectangular coordinates are (x,y)=(2,9) is in the 2nd quadrant of the plane, if we take r=x2+y2=4+81=85, then we need to add π radians to the output of the arctangent function to find the angle: θ=arctan(yx)+π=arctan(92)+π=arctan(92)+π.