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Technical Mathematics, Sixth Edition by Michael A. Calter Ph.D., Paul A. Calter

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15.6. Graphing in Polar Coordinates

Up to this point we have done all our graphing in the familiar rectangular coordinate system. We now introduce a new coordinate system, which is more useful than rectangular coordinates for some kinds of graphing. Most of our graphing will continue to be in rectangular coordinates, but in some cases polar coordinates will be more convenient.

Figure 15.33. Polar coordinates.

15.6.1. The Polar Coordinate System

The polar coordinate system (Fig. 15-33) consists of a polar axis, passing through point O, which is called the pole. The location of a point P is given by its distance r from the pole, called the radius vector, and by the angle θ, called the polar angle(sometimes called the vectorial angle or reference angle). The polar angle is called positive when measured counterclockwise from the polar axis, and negative when measured clockwise.

The polar coordinates of a point P are thus r and θ usually written in the form P(r, θ), or as (read "r at an angle of θ").

TI-83/84 graph of r = 8 sin θ, a circle. On TI calculators, polar mode is Pol on the menu. Selecting ZSquare will adjust the scales so that circles appear circular.

Example 27:

A point ...

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