How do you convert the Cartesian coordinates (-6, 13) to polar coordinates?

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How do you convert the Cartesian coordinates (-6, 13) to polar coordinates?

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Answer 1 · 2015-08-18T15:13:32

$(\sqrt{205}, arctan - \frac{6}{13})$ $(sqrt205, arctan-6/13)$

Explanation:

Using polar coordinates, it would be rcos $θ$ $theta$ = -6 and r sin $θ$ $theta$ =13.

Squaring and adding both these equations would give $r^{2} = 13^{2} + 6^{2}$ $r^2=13^2 +6^2$ , that is r= $\sqrt{205}$ $sqrt205$

Dividing these equations would give tan $θ = - \frac{6}{13}$ $theta= -6/13$ , that is $θ$ $theta$ = arc tan $(- \frac{6}{13})$ $(-6/13)$ . The polar coordinates are written as (r, $θ$ $theta$ ), hence we can write (-6, 13) accordingly.

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How do you convert the Cartesian coordinates (-6, 13) to polar coordinates?

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