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ss_8_1 - Section 8.1 Polar Coordinates As well as...

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Section 8.1 Polar Coordinates As well as rectangular cartesian coordinates, polar coordinates can also be used to locate points in two-dimensional space. It turns out that some equations and graphs are best expressed in polar coordinates and some in cartesian coordinates. The following diagrams show polar coordinate systems and some terminology used with polar coor- dinates. Just as a point’s location in two-dimensional space can be described by its cartesian ( x, y ) coordinates, a point can also be described by its polar ( r, θ ) coordinates. For example, the Pole in the following diagrams has ( r, θ )=(0 , 0) and ( x, y )=(0 , 0), and the point P in the diagrams has ( r, θ )=(2 , π 4 )and( x, y )=( 2 , 2). Polar coordinates ( r, θ ) There are some important conventions that must be followed when plotting polar coordinates. For example, when an angle is positive, then the angle is plotted with a counterclockwise motion, and when an angle is negative, the angle is plotted with a clockwise motion. When r is positive, r is plotted in the direction of the terminal side of the angle, and when r is negative, r is plotted in the direction opposite the angle’s terminal side. This information is tabulated below.
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_8_1 - Section 8.1 Polar Coordinates As well as...

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