Hence r z 117 and 2 2k 1k for integers k

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Unformatted text preview: y 2 = x2 + y 2 + x . Once again, we have performed some 10 Exercise 3 in Section 5.3, for instance . . . Here, ‘equivalent’ means they represent the same point in the plane. As ordered pairs, (3, 0) and (−3, π ) are different, but when interpreted as polar coordinates, they correspond to the same point in the plane. Mathematically speaking, relations are sets of ordered pairs, so the equations r2 = 9 and r = −3 represent different relations since they correspond to different sets of ordered pairs. Since polar coordinates were defined geometrically to describe the location of points in the plane, however, we concern ourselves only with ensuring that the sets of points in the plane generated by two equations are the same. This was not an issue, by the way, when we first defined relations as sets of points in the plane in Section 1.2. Back then, a point in the plane was identified with a unique ordered pair given by its Cartesian coordinates. √ 12 In addition to taking the tangent of both sides of an equation (There are infini...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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