Question

What are the polar coordinates for the point (1,-2) i got r = 5 but theta = arctan -2?

Answer 1

\[r=\sqrt{5}\]

Answer 2

yeah i got that far

Answer 3

and yes, in this case
\[\theta =\tan^{-1}(-2)\] because you are in quadrant 4

Answer 4

okay so arctan(-2) is correct?

Answer 5

yes. it is always the case that
\[\tan(\theta)=\frac{b}{a}\] but it is not always the case that
\[\theta=\tan^{-1}(\frac{b}{a})\]

Answer 6

because arctan only returns answers in
\[[-\frac{\pi}{2},\frac{\pi}{2}]\]so you need to be careful about what quadrant you are in