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Sagot :
The polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
In this question,
We have been given the cartesian coordinate (-6, -1)
We need to convert given cartesian coordinate to polar coordinates.
We know that the polar coordinates is of the form (r, θ)
where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
and θ is the angle associated with the coordinates which is given by θ = [tex]tan^{-1}(\frac{y}{x} )[/tex]
The magnitude of the given polar coordinate is,
⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
⇒ r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]
⇒ r = [tex]\sqrt{36+ 1}[/tex]
⇒ r = [tex]\sqrt{37}[/tex]
⇒ r = 6.08
And the angle associated with the coordinate is,
⇒ θ = [tex]tan^{-1}(\frac{-1}{-6} )[/tex]
⇒ θ = [tex]tan^{-1}(0.167 )[/tex]
⇒ θ = 9.48°
⇒ θ = 0.0523π
So, the polar coordinate is (6.08, 0.0523π)
Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
Learn more about the polar coordinates here:
https://brainly.com/question/16034289
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