How do you convert the cartesian coordinate (-5, -5) into polar coordinates?

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How do you convert the cartesian coordinate (-5, -5) into polar coordinates?

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Answer 1 · 2015-09-24T03:43:27

$(r, θ) = (5 \sqrt{2}, \frac{5 π}{4})$ $(r,theta)=(5sqrt(2),(5pi)/4)$

Explanation:

For $r$ $r$ , use the formula $r = \sqrt{x^{2} + y^{2}} = \sqrt{5^{2} + 5^{2}} = \sqrt{50} = \sqrt{25} \sqrt{2} = 5 \sqrt{2}$ $r=sqrt(x^2+y^2)=sqrt(5^2+5^2)=sqrt(50)=sqrt(25)sqrt(2)=5sqrt(2)$ .

For $θ$ $theta$ , note that the point $(x, y) = (- 5, - 5)$ $(x,y)=(-5,-5)$ is in the third quadrant. Hence, $θ = {tan}^{- 1} (\frac{y}{x}) + π = {tan}^{- 1} (1) + π = \frac{π}{4} + π = \frac{5 π}{4}$ $theta=tan^{-1}(y/x)+pi=tan^{-1}(1)+pi=pi/4+pi=(5pi)/4$ (adding or subtracting any whole number multiple of $π$ $pi$ to this also works for $θ$ $theta$ ).

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How do you convert the cartesian coordinate (-5, -5) into polar coordinates?

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