Question #13be9

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Answer 1 · 2017-01-06T07:41:22

The answer is $= (\frac{\sqrt{3}}{2}, \frac{3}{2})$ $=(sqrt3/2,3/2)$

To convert from polar coordinates $(r, θ)$ $(r,theta)$ to rectangular coordinates $(x, y)$ $(x,y)$ , we use the following equations

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsin theta$

Here,

$(r, θ) = (\sqrt{3}, - \frac{5 π}{3})$ $(r,theta)=(sqrt3,-(5pi)/3)$

$cos (- \frac{5 π}{3}) = \frac{1}{2}$ $cos(-(5pi)/3)=1/2$

$x = \sqrt{3} \cdot cos (- \frac{5 π}{3}) = \sqrt{3} \cdot \frac{1}{2} = \frac{\sqrt{3}}{2}$ $x=sqrt3*cos(-(5pi)/3)=sqrt3*1/2=sqrt3/2$

and

$sin (- \frac{5 π}{3}) = \frac{\sqrt{3}}{2}$ $sin(-(5pi)/3)=sqrt3/2$

$y = \sqrt{3} \cdot sin (- \frac{5 π}{3}) = \sqrt{3} \cdot \frac{\sqrt{3}}{2} = \frac{3}{2}$ $y=sqrt3*sin(-(5pi)/3)=sqrt3*sqrt3/2=3/2$

So, the rectangular coordinates are $= (\frac{\sqrt{3}}{2}, \frac{3}{2})$ $=(sqrt3/2,3/2)$