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The process of conversion of rectangular co-ordinates (x, y) to polar co-ordinates `(r, theta)` is as follows `r = sqrt(x^2 + y^2)` and `theta = tan^-1(y/x)`
For the point (1, 1) the polar co-ordinates are `r = sqrt(1 + 1) = sqrt 2` and `theta = tan^-1(1/1) = 45^@`
The polar co-ordinates of (1, 1) are `(sqrt 2, 45^@)`
The above answer is correct as long as the point lies in the first quadrant but following the same process we obtain the same result for point (-1,-1). i.e. r = sqrt(2) and angle = 45 degrees which is not true. In this case angle = 135 degrees.
Hence it is important to establish the quadrant in which the point (x,y) lies. In case of point (-1,-1), we know that x and y are both negative and therefore the point lies in the third quadrant. In conversion from rectangular coordinates to polar coordinates this finer point has to be taken in to account while determining the angle. tan-1(1) is equal to 1 for both 45 degrees and 135 degrees but we have to opt for 135 degrees because the point lies in the 3rd quadrant and not in the first quadrant.
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