Question

Convert the cartesian coordinate (-6,-1) to polar coordinates, 0 ≤ θ < 2 π , r > 0 0≤θ<2π, r>0

Answer 1

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 = $\sqrt{x^{2}+ y^{2} }$

and θ is the angle associated with the coordinates which is given by           θ =  $tan^{-1}(\frac{y}{x} )$

The magnitude of the given polar coordinate is,

⇒ r = $\sqrt{x^{2}+ y^{2} }$

⇒  r = $\sqrt{(-6)^{2}+ (-1)^{2} }$

⇒ r = $\sqrt{36+ 1}$

⇒ r = $\sqrt{37}$

⇒ r = 6.08

And the angle associated with the coordinate is,

⇒ θ =  $tan^{-1}(\frac{-1}{-6} )$

⇒ θ =  $tan^{-1}(0.167 )$

⇒ 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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