Question

Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 3 comma 5 pi divided by 3. (-3, (5pi/3))

Answer 1

Answer:

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This is the actual answer: ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2

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Answer 2

Answer:

see explanation

Step-by-step explanation:

To convert from polar to rectangular coordinates

that is (r, Θ ) → (x, y), then use

x = r cosΘ and y = r sinΘ

here r = 3 and Θ = $\frac{5\pi }{3}$, hence

x = 3 cos($\frac{5\pi }{3}$)

  =  3 cos($\frac{\pi }{3}$)

  =  3 × $\frac{1}{2}$ = $\frac{3}{2}$

y = 3 sin($\frac{5\pi }{3}$)

  = - 3 sin($\frac{\pi }{3}$)

  = - 3 × $\frac{\sqrt{3} }{2}$ = - $\frac{3\sqrt{3} }{2}$

(3, $\frac{5\pi }{3}$) → ($\frac{3}{2}$, - $\frac{3\sqrt{3} }{2}$)