By applying the relationships between rectangular and polar systems of coordinates we determine that (x, y) = (-3, 0) is equivalent to (r, θ) = (3, π).
How to convert rectangular coordinates into polar form
Rectangular coordinates represent a point in terms of orthogonal distances ("horizontal" and "vertical"), whereas the polar coordinates are represented by a distance with respect to origin (r) and a standard angle (θ). There is the following relationship between rectangular and polar systems of coordinates:
(x, y) = r · (cos θ, sin θ) (1)
Where [tex]r = \sqrt{x^{2}+ y^{2}}[/tex] and [tex]\theta = \tan^{-1} \left(\frac{y}{x} \right)[/tex].
If we know that (x, y) = (-3, 0), then the polar form of the coordinates are:
[tex]r = 3[/tex], [tex]\theta = \pi[/tex]
By applying the relationships between rectangular and polar systems of coordinates we determine that (x, y) = (-3, 0) is equivalent to (r, θ) = (3, π).
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