The polar coordinate would be (4.47, -0.46).
What is the difference between cartesian coordinates and polar coordinates?
Although Cartesian coordinates can be utilized in three dimensions (x, y, and z), polar coordinates only identify two dimensions (r and θ). If a third axis, z (height), exists added to polar coordinates, the coordinate system exists directed to as cylindrical coordinates (r, θ, z).
Given:
Let the point be (4,-2).
To convert, cartesian coordinates (x, y) to polar coordinates (r, [tex]$\theta[/tex]),
[tex]$r &=\sqrt{x^{2}+y^{2}} \\[/tex]
[tex]$\theta &=\tan ^{-1} \frac{y}{x} \\$[/tex]
[tex]$ r &=\sqrt{4^{2}+(-2)^{2}} \\[/tex]
[tex]${data-answer}amp;=\sqrt{16+4} $[/tex]
[tex]${data-answer}amp;=\sqrt{20}[/tex]
= 4.47
[tex]$\theta &=\tan ^{-1} \frac{-2}{4} \\[/tex]
[tex]${data-answer}amp;=\tan ^{-1} \frac{-1}{2}=-0.46 \\[/tex]
The polar coordinate would be (4.47,-0.46)
Therefore, the correct answer is option c. r = 4.47, [tex]$\theta[/tex] = -0.46
To learn more about cartesian coordinates and polar coordinates
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