How do you convert (-sqrt3,-1) into polar coordinates?

1 Answer
Alan P.
Mar 22, 2018

Cartesian form: (x,y)=(-sqrt(3),-1)
color(white)("xxx")rarrcolor(white)("xx")Polar form: (r,theta)=(2,240^circ)

Explanation:

The ratio of side lengths implies the common angle 60^circ (or pi/3 if you prefer radians) as the reference angle.

The terminal point (since both coordinates are negative) falls in Quadrant III, so the angle is 180^circ+60^circ=240^circ.

The radius (distance from the origin is given by the Pythagorean Theorem as sqrt((-1)^2+(-sqrt(3))^2)=2
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