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

$(r,theta)=(5sqrt(2),(5pi)/4)$

Explanation:

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

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

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

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