Calculus Notes 11.3 - Calculus-Stewart Dr Berg Summer 09...

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Calculus- Stewart Dr. Berg Summer ‘09 Page 1 11.3 11.3 Polar Coordinates The position of a point in a plane is determined by two numbers. We normally use Cartesian coordinate systems, but there are others. Many curves are more easily described using polar coordinates that give the angle of a ray through the point and the distance from the origin. Definition Fix a point called the pole and extend a ray to the right, which we call the pole axis . The polar coordinates of a point are a pair of real numbers ( r , θ ) where θ is the angle in radians between the polar axis and a ray from the pole through the point and r is the distance. It is convenient to define (0, θ ) to be the pole for any angle θ . It is also convenient to allow r to be negative and take that to mean going in the opposite direction. ( r , θ ) (– r , θ ) Notice that, unlike Cartesian coordinates, polar coordinates are not unique. The origin is represented by (0, θ ) where θ can be any angle. Also, a point with coordinates ( r , θ ) can also be represented by ( r ,
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