How do you convert $(3, 2 \frac{π}{3})$ $(3, 2pi/3)$ into rectangular forms?

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How do you convert $(3, 2 \frac{π}{3})$ $(3, 2pi/3)$ into rectangular forms?

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Answer 1 · 2015-12-01T12:01:19

polar form: $(3, \frac{2 π}{3}) \to$ $(3,(2pi)/3) rarr$ rectangular form: $(- \frac{3}{2}, \frac{3 \sqrt{3}}{2})$ $(-3/2,(3sqrt(3))/2)$

Explanation:

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

$x = r \cdot cos (θ) = 3 \cdot cos (\frac{2 π}{3}) = 3 \cdot (- \frac{1}{2}) = - \frac{3}{2}$ $x= r*cos(theta) = 3*cos((2pi)/3) = 3*(-1/2) = -3/2$

$y = r \cdot sin (θ) = 3 \cdot sin (\frac{2 π}{3}) = 3 \cdot (\frac{\sqrt{3}}{2}) = \frac{3 \sqrt{3}}{2}$ $y = r*sin(theta)=3*sin((2pi)/3) = 3*(sqrt(3)/2) = (3sqrt(3))/2$
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How do you convert $(3, 2 \frac{π}{3})$ $(3, 2pi/3)$ into rectangular forms?

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