How do you convert the Cartesian coordinates (-2,-2) to polar coordinates?

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How do you convert the Cartesian coordinates (-2,-2) to polar coordinates?

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Answer 1 · 2015-10-22T12:52:51

$(x, y) = (- 2, - 2) \Leftrightarrow (r, θ) = (2 \sqrt{2}, \frac{5 π}{4})$ $(x,y) = (-2,-2) iff (r,theta) = (2sqrt(2),(5pi)/4)$

Explanation:

Given $(x, y) = (- 2, - 2)$ $(x,y) = (-2,-2)$

Since $x = y$ $x=y$ we have a reference angle of $\frac{π}{4}$ $pi/4$
and since both $x$ $x$ and $y$ $y$ are negative the point is in Quadrant III
$\Rightarrow θ = \frac{5 π}{4}$ $rArr theta = (5pi)/4$

The radius, $r$ $r$ can be calculated using the Pythagorean Theorem:
$XX r = \sqrt{{(- 2)}^{2} + {(- 2)}^{2}} = 2 \sqrt{2}$ $color(white)("XX")r=sqrt((-2)^2+(-2)^2) = 2sqrt(2)$

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How do you convert the Cartesian coordinates (-2,-2) to polar coordinates?

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