12.1.3 Rotations (continued)
Example 4 Engineering Application
The coordinates of a point rotating at a particular rate is determined after a time interval in this application example. The beginning coordinates of the point (a bucket on a mill wheel) and its rate of rotation are given. The center of rotation is given as the origin. A complete rotation about the origin takes 5 seconds, so after 2 seconds the point will have rotated through (2/5)360° = 144°. To find the coordinates of the bucket at this point, construct a right triangle with leg lengths equal to the x and y coordinates and hypotenuse equal to the radius, 6 ft. The angle at the origin of the triangle is 180° − 144° = 36°. Calculate the x and y coordinates using the sine and cosine of the 36° angle. The coordinates of the bucket’s location after 2 seconds of rotation are approximately ( − 4.9, 3.5).
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