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Rotation and the Unit Circle

The unit circle is a convenient vehicle for working with rotation and other trigonometric activities. A unit circle is a circle that you graph with its center on the origin of a Cartesian plane and its radius set to 1. Figure 12.13 illustrates a unit circle. Such a representation of a circle proves useful when you seek a convenient way to relate measurements of angles to measurements of rotation. When you set the diameter of a circle to 1, if an angle measures, for example, (90°), then the radian measure of the angle also tells you the length of the arc that the angle designates on the perimeter of the circle. At the ...

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