In the polar coordinate system, each point also has two values associated with it: r r and θ. Note that every point in the Cartesian plane has two values (hence the term ordered pair) associated with it. ![]() This correspondence is the basis of the polar coordinate system. This observation suggests a natural correspondence between the coordinate pair ( x, y ) ( x, y ) and the values r r and θ. The angle between the positive x x-axis and the line segment has measure θ. The line segment connecting the origin to the point P P measures the distance from the origin to P P and has length r. The point P P has Cartesian coordinates ( x, y ). To find the coordinates of a point in the polar coordinate system, consider Figure 7.27. In this section we see that in some circumstances, polar coordinates can be more useful than rectangular coordinates. ![]() The polar coordinate system provides an alternative method of mapping points to ordered pairs. This is called a one-to-one mapping from points in the plane to ordered pairs. The rectangular coordinate system (or Cartesian plane) provides a means of mapping points to ordered pairs and ordered pairs to points. ![]() 7.3.5 Identify symmetry in polar curves and equations.7.3.4 Convert equations between rectangular and polar coordinates.7.3.3 Sketch polar curves from given equations.7.3.2 Convert points between rectangular and polar coordinates.7.3.1 Locate points in a plane by using polar coordinates.
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