Question

I am currently converting Rectangular points into Polar points. The point is (3,-1)
I have so far converted this much:
X= 3 Y=-1
T=Theta
tan T= Y/X
T=arctan(-3)
T=?
T=?

x^2+y^2=r^2
r=+or- sqrt 10

Answer 1

\[\tan \theta = \left(\begin{matrix}x \\ y\end{matrix}\right)\]
\[\theta = \arctan (-3)\]
\[\theta = ?\]
\[\theta = ?\]

Answer 2

I meant \[\left(\begin{matrix}y \\ x\end{matrix}\right)\]
sorry.

This might go under Unit Circle Pre-Calc stuff.

Answer 3

right so the polar coordinates of point (3,-1) is (sqrt10 , arctan(-1/3))

Answer 4

would there be a specific coordinate on the unit circle?, such as \[\left(\begin{matrix}\pi \\ 3\end{matrix}\right)\]
or would the general statement of arctan be good?

because I know arctan(-1)
\[\theta = \left(\begin{matrix}\pi \\ 4\end{matrix}\right)\]
and
\[\theta = \left(\begin{matrix}3\pi \\ 4\end{matrix}\right)\]

Answer 5

no not for -1/3 , the base angles pi/6 , pi/4 , pi/3 have tangents of 1/sqrt3 , 1 , sqrt3

you can only approximate angle with calculator

Answer 6

http://www.wolframalpha.com/input/?i=arctan%28-1%2F3%29