Trigonometry of General Triangles and Trigonometric Functions — Test
Question 4 • Mathematics III
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h , the height in feet of the end of one blade, as a function of time, t , in seconds? Assume that the blade is pointing to the right, parallel to the ground at t is equal to 0 seconds, and that the windmill turns counterclockwise at a constant rate.
Answer
A
h is equal to negative 10 sine pi t plus 35
B
h is equal to 10 sine open paren pi over 15 t close paren plus 35
C
h is equal to 10 sine pi t plus 35
D
h is equal to negative 10 sine open paren pi over 15 t close paren plus 35
Explanation
The blade’s tip moves 10 feet above and below the axis, so the height has amplitude 10 and a midline of 35 feet. Two rotations per minute is one rotation every 30 seconds, giving angular speed 2π/30 = π/15 radians per second. Since the blade starts pointing right and turns counterclockwise, its vertical displacement starts at 0 and increases, so the model is h = 10 sin(πt/15) + 35, choice D.
AI-written and checked against the verified answer.