Question

How do you convert `(11,-9)` into polar coordinates?

Answer 1

`(sqrt202,tan^-1(-9/11)+2pi) or (14.2,5.60^c)`

Explanation:

`(x,y)->(r,theta);(r,theta)=(sqrt(x^2+y^2),tan^-1(y/x))`

`r=sqrt(x^2+y^2)=sqrt(11^2+(-9)^2)=sqrt(121+81)=sqrt202~~14.2`

`theta=tan^-1(-9/11)`

However, `(11,-9)` is in quadrant 4, and so we must add `2pi` to our answer.

`theta=tan^-1(-9/11)+2pi ~~5.60^c`

`(sqrt202,tan^-1(-9/11)+2pi) or (14.2,5.60^c)`