08-08-2014, 11:22 PM
For convenience, we begin with a given xy -coordinate system and then take the origin as the pole and the nonnegative x -axis as the polar axis. Given the pole O and the polar axis, the point P with polar coordinates r and θ , written as the ordered pair (r,θ
, is located as follows. First find the terminal side of the angle θ , given in radians, where θ is measured counterclockwise (if θ>0 ) from the x -axis (the polar axis) as its initial side. If r≥0 , then P is on the terminal side of this angle at the distance r from the origin. If r<0 , then P lies on the terminal side of this angle at the distance r from the origin. If r<0 , then P lies on the ray opposite the terminal side at the distance ∣r∣=-r>0 from the pole. The radial coordinate r can be described as the directed distance from P the pole along the terminal side of the angle θ . Thus, if r is positive, the point P lies in the same quadrant as θ , whereas if r is negative, then P lies in the opposite quadrant. If r=0 , the angle θ does not matter; the polar coordinates (0,θ represent the origin whatever the angular coordinate θ might be. The origin, or pole, is the only point for which r=0 .
, is located as follows. First find the terminal side of the angle θ , given in radians, where θ is measured counterclockwise (if θ>0 ) from the x -axis (the polar axis) as its initial side. If r≥0 , then P is on the terminal side of this angle at the distance r from the origin. If r<0 , then P lies on the terminal side of this angle at the distance r from the origin. If r<0 , then P lies on the ray opposite the terminal side at the distance ∣r∣=-r>0 from the pole. The radial coordinate r can be described as the directed distance from P the pole along the terminal side of the angle θ . Thus, if r is positive, the point P lies in the same quadrant as θ , whereas if r is negative, then P lies in the opposite quadrant. If r=0 , the angle θ does not matter; the polar coordinates (0,θ represent the origin whatever the angular coordinate θ might be. The origin, or pole, is the only point for which r=0 .