MCT4C
Working with Trig Functions: Applications
1. A small windmill has its centre 6 metres above the ground and the blades are 2 metres in length. In a
steady wind, each blade makes a complete rotation in 12 seconds.
a) If the rotation begins at the highest possible point, sketch a graph of the height of the tip of the blade
above the ground, versus time, for TWO cycles.
b) Determine a trigonometric equation to represent the height of the tip of one blade of the windmill over
time.
c) What is the height above the ground at:
3 seconds? __________ 18 seconds? ________
d) How would the equations change if a full rotation took 20 seconds?
e) How would the original equations change if each blade was 3 metres in length?
2. At a country fair, the Ferris wheel has a radius of 11 m and the base of the wheel, the loading area, is
2.5 m above the ground. The wheel completes one revolution every 16 seconds.
a) Graph a rider’s height above the ground, in metres, versus the time, in seconds,
during 32 seconds of the ride. The rider begins at the lowest position on the wheel.
b) Determine a trigonometric equation to represent the height of the ferris wheel over time.
c) What is the height of a rider after 10 seconds? 35 seconds?
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3. A rung on a hamster wheel has a radius of 25cm. It makes one complete revolution in 3 sec. The axel
of the hamster wheel is 27cm above the ground.
a) Graph the height of the rung above the ground during two complete revolutions, beginning when the
rung is closest to the ground.
b) Determine a sine OR cosine function to model this situation.
4. The water depth in a harbour is 26 m high at high tide and 12 m a low tide. One cycle is completed every 12
hours. High tide occurs at midnight. (a sketch is optional)
a) Determine an equation to model this situation (using sine or cosine)
b) Determine the length of time in one 24 hour period that the depth of the water is at least 23 m.
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