The polar coordinates is [tex](12, \frac{\pi }{9})[/tex].
What is polar coordinate system?
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
How to convert rectangular coordinates to polar coordinates?
To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula
tanθ = y/x and [tex]r=\sqrt{x^{2} +y^{2} }[/tex]
According to the given question
We have a rectangular coordinates (11, -4)
⇒ x = 11 and y = -4
Therefore,
[tex]r=\sqrt{(11)^{2}+(-4)^{2} }[/tex]
⇒ [tex]r =\sqrt{121+16} =\sqrt{137} =11.7[/tex]
⇒ [tex]r =12[/tex]
And,
tanθ = [tex]\frac{y}{x}[/tex]
⇒tanθ =[tex]\frac{-4}{11}[/tex]
⇒tanθ = -0.36
⇒ θ =[tex]tan^{1} (-0.36)[/tex]
⇒ θ = 19.8 degrees Or θ = 20 degrees
⇒ θ = [tex]\frac{\pi }{9}[/tex]
Therefore, the polar coordinates is [tex](12, \frac{\pi }{9})[/tex].
Learn more about polar coordinates here:
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