Question

How do you convert the Cartesian coordinates (-6, 13) to polar coordinates?

Answer 1

`(sqrt205, arctan-6/13)`

Explanation:

Using polar coordinates, it would be rcos`theta`= -6 and r sin`theta`=13.

Squaring and adding both these equations would give `r^2=13^2 +6^2`, that is r= `sqrt205`

Dividing these equations would give tan`theta= -6/13`, that is `theta`= arc tan`(-6/13)`. The polar coordinates are written as (r, `theta`), hence we can write (-6, 13) accordingly.