How do you find the rectangular coordinates given the polar coordinates $(- 2, \frac{4 π}{3})$ $(-2,(4pi)/3)$ ?

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Answer 1 · 2016-11-21T10:49:08

The rectangular coordinates are $= (1, - \sqrt{3})$ $=(1,-sqrt3)$

To convert from polar coordinates $(r, θ)$ $(r,theta)$ to recangular coordinates $(x, y)$ $(x,y)$

We use the following

$x = r cos θ$ $x=rcostheta$

and $y = r sin θ$ $y=rsintheta$

Here, $(r, θ) = (- 2, \frac{4 π}{3})$ $(r,theta)= (-2,(4pi)/3)$

$:. x=-2cos((4pi)/3)$

and $y=-2sin((4pi)/3)$

$cos((4pi)/3)=-1/2$ and $sin((4pi)/3)=sqrt3/2$

Therefore, $(x,y)=(1,-sqrt3)$

How do you find the rectangular coordinates given the polar coordinates (-2,(4pi)/3)(−2,4π3)(-2,(4pi)/3)?