Stitz-Zeager_College_Algebra_e-book

We have established the following theorem 6 turn r ed

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Unformatted text preview: ntation for P with r = −3, we may choose any angle coterminal with π π − π . We choose θ = 74 for our final answer −3, 74 . 4 P 3, 3π 4 P −3, θ= 7π 4 3π 4 Pole θ= 7π 4 Pole Now that we have had some practice with plotting points in polar coordinates, it should come as no surprise that any given point expressed in polar coordinates has infinitely many other representations in polar coordinates. The following result characterizes when two sets of polar coordinates determine the same point in the plane. It could be considered as a definition or a theorem, depending on your point of view. We state it as a property of the polar coordinate system. Equivalent Representations of Points in Polar Coordinates Suppose (r, θ) and (r , θ ) are polar coordinates where r = 0, r = 0 and the angles are measured in radians. Then (r, θ) and (r , θ ) determine the same point P if and only if one of the following is true: • r = r and θ = θ + 2πk for some integer k • r = −r and θ = θ + (2k + 1)π for some integer k All polar coordinates of the form (0, ...
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