Hello, Ivy!
Sorry, Prove it . . . $\displaystyle r$ can be negative.
Convert (-3,4) to polar coordinates.
I get (5, -4.140), but it's wrong.
The solution is supposed to be (5, 2.21) or (-5, 5.36).
Why do I keep getting the wrong answer?
. . How did you get that angle? Code:
(-3,4) |
* |
:\ |
4: \5|
: \|
- - + - + - - - -
3 |
We see that: .$\displaystyle r \,=\,5.$
The angle is: .$\displaystyle \theta \:=\:\tan^{-1}\left(\text{-}\tfrac{4}{3}\right) \:\approx\:\text{-}0.927\text{ radians}$
This translates to positive angles of: .$\displaystyle 2.21\text{ and }5.36\text{ radians.}$
You should be aware that there are an infinite number of ways
. . to designate a point in polar coordinates.
Two of the ways are: .$\displaystyle (2.21,\,5)$ and $\displaystyle (-5,\,5.36)$
Recall how polar coordinates are plotted.
The first $\displaystyle (5,\,2,21)$ tells us:
. . stand at the pole (origin), face East, turn 2.21 radians CCW
. . and walk forward 5 units.
This places us at the point in Quadrant 2.
The second $\displaystyle (-5,\,5.36)$ tells us:
. . stand at the pole, face East, turn 5.36 radians CCW
. . and walk backward 5 units.
This places us at the same point.