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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Measuring Angles

Degrees, radians, rotations

Note: Problems 1.9–1.11 refer to angle ABC in the diagram below. The angle’s initial side and terminal side both lie on the positive x-axis.

1.9    Express the measure of angle ABC in revolutions.

According to the arrowed arc at the center of this diagram, angle ABC begins at the positive x-axis, rotates exactly once around the coordinate plane, and terminates where it began, at the positive x-axis. To visualize this angle, stand up and point at a specific spot on the wall. Then, while standing in the same location, slowly turn in the counterclockwise direction, keeping your arm straight in front ...

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