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Hannah L.

asked • 06/23/16

Finding the distance from ceiling to each point in the clock and finding an equation with cosine or sine

2) Clock #2: A clock has a radius of 6 inches. The center is 14.5 inches below the ceiling. Measure the distance from the ceiling to the tip of the hour hand at each hour beginning at 12 (which is t=0). For example, at t=0, d=8.5 inches. Complete the table and round your answers to the nearest hundreth if needed.

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Gregg O. answered • 06/23/16

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Hannah L.

I understood how to find the 12 o clock, 3 o clock, 6 o clock and 9 o clock, I am confused how to find the 1 ,2,4,5,7,8,10, and 11 o clock 
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06/23/16

Gregg O.

Hi again Hannah.  Let's imagine the hour positions as regular marks along the perimeter of the circle.  How many of these marks are there?  12.  This divides the circle into 12 regular partitions.  Imagine an angle with vertex at the center of the clock, and edges intersecting the circle at consecutive numbers (11 and 12, 12 and 1, etc.).  What is the measure of this angle?  360/12 = 30 degrees.  Starting at 3 o'clock, each hour mark, when rotating counterclockwise is an increment of 30 degrees.  So the height of the 2 o'clock mark is sin(30) above the origin; the height of the 1 o'clock mark is sin (2*30) units above the origin.  Follow this pattern to determine heights relative to the origin.  From there, you can find the distance to the horizontal line above the origin. 
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06/23/16

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