The height, h , in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t , in hours? Assume that the time at t is equal to 0 is 12:00 a.m.
Answer
A
h is equal to cosine of open paren pi over 12 t close paren plus 9
B
h is equal to 0 point 5 cosine open paren pi over 6 t close paren plus 9 point 5
C
h is equal to 0 point 5 cosine open paren pi over 12 t close paren plus 9 point 5
D
h is equal to cosine of open paren pi over 6 t close paren plus 9
Explanation
The height ranges from 9 to 10 feet, so its midline is (9 + 10)/2 = 9.5 feet and its amplitude is (10 − 9)/2 = 0.5 feet. The hour hand completes one cycle every 12 hours, giving angular frequency 2π/12 = π/6. At t = 0, the hand points to 12 and is at its greatest height, so a cosine model starts at its maximum: h = 0.5 cos(πt/6) + 9.5.
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