Question

What is the polar form of `(-1,12)`?

Answer 1

`(sqrt145, 94.76^o)`

Explanation:

`x=-1, y=12;r = sqrt(x^2+y^2)=sqrt145`.

`theta` satisfying both `cos theta=x/r=-1/sqrt145` and `sin theta =y/r=12/sqrt145` is

94,76^o#,
in the second quadrant in which cosine is negative and sine is positive.

`sin (180^o-theta)=sin theta`. Calculator display for `sin^(-1)(12/sqrt145)` is `85.24^o`, nearly.
Choose `theta = 180^o-85.24^o=94.76^o=cos^(-1)(-1/sqrt145)`.