When you first learn to relate an angle to a circle, your activity often begins with an orientation toward the circle that begins with the Cartesian plane. As Figure 12.6 illustrates, you extend a line (r) from the center of a circle to its perimeter. Using the standard form of an angle, you identify the x axis extending to the right from the origin as the initial side of the angle. The line that creates the angle constitutes the terminal side. You measure the angle (θ) created by the initial side and the terminal sides in degrees that describe the perimeter of the circle.

The measure of an angle θ has no maximum value in degrees. If it extends upward from the ...

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