What is the Cartesian form of $(6, - \frac{π}{6})$ $( 6,-pi/6 )$ ?

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What is the Cartesian form of $(6, - \frac{π}{6})$ $( 6,-pi/6 )$ ?

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Answer 1 · 2016-10-08T07:45:25

Cartesian form of $(6, - \frac{π}{6})$ $(6,-pi/6)$ is $(3 \sqrt{3}, - 3)$ $(3sqrt3,-3)$

Explanation:

Polar coordinates $(r, θ)$ $(r,theta)$ are equivalent to Cartesian Coordinates $(r cos θ, r sin θ)$ $(rcostheta,rsintheta)$

Hence polar coordinates $(6, - \frac{π}{6})$ $(6,-pi/6)$ are equivalent to Cartesian Coordinates $(6 \times cos (- \frac{π}{6}), 6 \times sin (- \frac{π}{6}))$ $(6xxcos(-pi/6),6xxsin(-pi/6))$

i.e. $(6 \times cos (\frac{π}{6}), 6 \times - sin (\frac{π}{6}))$ $(6xxcos(pi/6),6xx-sin(pi/6))$

or $(6 \times \frac{\sqrt{3}}{2}, - 6 \times \frac{1}{2})$ $(6xxsqrt3/2,-6xx1/2)$

or $(3 \sqrt{3}, - 3)$ $(3sqrt3,-3)$

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What is the Cartesian form of $(6, - \frac{π}{6})$ $( 6,-pi/6 )$ ?

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Explanation:

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What is the Cartesian form of $(6, - \frac{π}{6})$ $( 6,-pi/6 )$ ?