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 = [tex]\frac{5\pi }{3}[/tex], hence
x = 3 cos([tex]\frac{5\pi }{3}[/tex])
= 3 cos([tex]\frac{\pi }{3}[/tex])
= 3 × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex]
y = 3 sin([tex]\frac{5\pi }{3}[/tex])
= - 3 sin([tex]\frac{\pi }{3}[/tex])
= - 3 × [tex]\frac{\sqrt{3} }{2}[/tex] = - [tex]\frac{3\sqrt{3} }{2}[/tex]
(3, [tex]\frac{5\pi }{3}[/tex]) → ([tex]\frac{3}{2}[/tex], - [tex]\frac{3\sqrt{3} }{2}[/tex])
