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How do you convert $(- \sqrt{3}, - 1)$ $(-sqrt3,-1)$ into polar coordinates?

1 Answer

Mar 22, 2018

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

Explanation:

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

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

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