Calculus Notes 11.3

# 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 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, ) to be the pole for any angle . 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, ) where can be any angle. Also, a point with coordinates ( r , ) can also be represented by ( r , + 2 n π )

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## This note was uploaded on 06/06/2010 for the course M 408 taught by Professor Hodges during the Spring '08 term at University of Texas at Austin.

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

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