Describing Periodic Motion
The hour hand of the large clock on the wall in Union Station measures 24 inches in length. At noon, the tip of the hour hand is 30 inches from the ceiling. At 3 PM, the tip is 54 inches from the ceiling, and at 6 PM, 78 inches. At 9 PM, it is again 54 inches from the ceiling, and at midnight, the tip of the hour hand returns to its original position 30 inches from the ceiling. Let equal the distance from the tip of the hour hand to the ceiling hours after noon. Find the equation that models the motion of the clock and sketch the graph.
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OpenStax, Precalculus 2e · §7.6 Modeling with Trigonometric Functions · Example 5
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