Home > Precalculus > Converting Coordinates from Rectangular to Polar

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

Answer 1

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

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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.