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

1 Answer
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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