Question

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)`

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`