Answer:
see explanation
Step-by-step explanation:
To convert from rectangular to polar coordinates, that is
(x, y ) → (r, Θ )
r = [tex]\sqrt{x^2+y^2}[/tex]
Θ = [tex]tan^{-1}[/tex]([tex]\frac{y}{x}[/tex])
Given (- [tex]\sqrt{3}[/tex], - 1 ), then
r = [tex]\sqrt{(- [tex]\sqrt{3}[/tex])^2 + (-1)^2
= [tex]\sqrt{3+1}[/tex]
= [tex]\sqrt{4}[/tex] = 2 and
Θ = [tex]tan^{-1}[/tex]( [tex]\frac{-1}{-\sqrt{3} }[/tex] = [tex]tan^{-1}[/tex]( [tex]\frac{1}{\sqrt{3} }[/tex] = 30°
The rectangular coordinate point is in the third quadrant, thus Θ must be in the third quadrant, that is
Θ = 180° + 30° = 210°
Thus (r, Θ ) = (2, 210° )
