What are the polar coordinates of (1,-2) and how do you find them?

AI Thread Summary
To convert the Cartesian coordinates (1, -2) to polar coordinates, the calculations yield (√5, arctan(-2)) and (-√5, arctan(-2) + π). The value of arctan(-2) is approximately -63.43 degrees, which is not within the required range of 0 to 2π. To convert this angle to the correct range, adding 360 degrees (or 2π radians) gives a valid angle. The final polar coordinates are (√5, 296.57 degrees) for r > 0 and (-√5, 116.57 degrees) for r < 0.
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Homework Statement



Convert (1,-2) to polar coordinates find one representation with r >0 and one with r <0. Also 0<= theta <= 2 PI

Homework Equations



I used tantheta = y /x , and x^2 +y^2 = r^2

The Attempt at a Solution



I got (sqrt(5) , arctan(-2)) , (-sqrt(5) , arctan(-2) + pi )
Is this OK?
 
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Does arctan(-2) satisfy 0 <= theta <= 2 pi?
 
I think so it is -63.43 degrees in my calculator and I forget how arctan comes back in the calculator but if I add 180 to that it is still only 116. I forget where is comes back to the domain on the calculator I mean.
 
But -63.43° is not in the interval [0°, 360°]. That was essentially what SteamKing was objecting to.
 
OH opps. OK so add 360 to it. Then I'm good right?
 
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