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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