How do you find the polar coordinate for (3, -5)?

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Answer 1 · 2016-02-09T18:17:08

#sqrt34/_-59^@#

To convert rectangular co-ordinates #(x,y)# into polar co-ordinates #(r,theta)=r/_theta#, we use the transformations

#r=sqrt(x^2+y^2)and theta=tan^(-1)(y/x)#.

So in this particular case we get :

#r=sqrt(3^2+(-5)^2)=sqrt34#

#theta=tan^(-1)(-5/3)=-59^@#

This point is indeed in the 4th quadrant and hence its polar representation is #sqrt34/_-59^@#.