## Going from polar coor. to cartesian coor.

Hello, I recently run into a problem. Lets say I have the point (a,b) and (-a,-b). The, I know that θ_1 = atan(b/a) and θ_2 = atan((-b)/(-a)) = θ_1.

But, what if I want to go back to Cartesian coordinates? If I assume r = 1,
a = cos(θ_1) and b = sin(θ_1) while
-a = cos(θ_2) and b = sin(θ_2).

I am sure this is very simple and it has to do with the fact that the range of atan is (-π/2,π/2). But is there a way of getting back the -a? Could I just add π to the angle whenever a and b are negatives?
 Recognitions: Science Advisor Atan is multivalued, so you need to use more information to get the angle.

 Quote by Marioqwe Hello, I recently run into a problem. Lets say I have the point (a,b) and (-a,-b). The, I know that θ_1 = atan(b/a) and θ_2 = atan((-b)/(-a)) = θ_1. But, what if I want to go back to Cartesian coordinates? If I assume r = 1, a = cos(θ_1) and b = sin(θ_1) while -a = cos(θ_2) and b = sin(θ_2). I am sure this is very simple and it has to do with the fact that the range of atan is (-π/2,π/2). But is there a way of getting back the -a? Could I just add π to the angle whenever a and b are negatives?
In a word, yes. If a and b are both negative, then the point is in the third quadrant and you would need to add ∏ to atan(b/a) to derive θ_2. [Alternately you could decide to use a non-canonical polar representation with a negative value for r].

And yes, ignoring your sign omission, -a = cos(θ_2) and -b = sin(θ_2).

Some math libraries have a two-argument "atan2" function that figures the quadrants out for you so that the range of the atan2 is the full -∏ (exclusive) to +∏ (inclusive). This function also avoids the divide by zero problem for points on the y axis.

http://en.wikipedia.org/wiki/Atan2

## Going from polar coor. to cartesian coor.

I can certainly use atan2. Thank you.

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 Quote by mathman Atan is multivalued, so you need to use more information to get the angle.
atan isn't multivalued- usually the format is: atan(y/x);

atan2 is multivalued... (wikipedia link to definition of atan2 in terms of extension of atan function)

Recognitions: