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

1 Answer
Trevor Ryan.
Feb 9, 2016

sqrt34/_-59^@

Explanation:

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^@.

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