Question

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

Answer 1

`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^@`.