Hand out worksheet for next 2 examples. - My Math Site€¦ · 6) 3U Modeling Periodic Functions...
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6) 3U Modeling Periodic Functions Day 2.notebook 1 December 02, 2015 May 236:38 PM Trigonometry Part II Modeling Periodic Functions Day 2 By the end of this lesson you will be able to take a word problem and model the situation with a trig function. Learning Goal Nov 304:12 PM Hand out worksheet for next 2 examples. May 68:38 AM Example 1 . Ali's shop teacher was discussing table saws. The teacher produced two different graphs for two different types of saw. In each case, the graphs show the height of one tooth on the circular blade relative to the cutting surface of the saw in terms of time. Examine the graphs and answer the following questions. May 68:43 AM a) What is the maximum height of each blade? b) c) d) W
Transcript of Hand out worksheet for next 2 examples. - My Math Site€¦ · 6) 3U Modeling Periodic Functions...
6) 3U Modeling Periodic Functions Day 2.notebook
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December 02, 2015
May 236:38 PM
Trigonometry Part IIModeling Periodic Functions Day 2
By the end of this lesson you will be able to take a word problem and model the situation with a trig function.
Learning Goal
Nov 304:12 PM
Hand out worksheet for next 2 examples.
May 68:38 AM
Example 1. Ali's shop teacher was discussing table saws. The teacher produced two different graphs for two different types of saw. In each case, the graphs show the height of one tooth on the circular blade relative to the cutting surface of the saw in terms of time. Examine the graphs and answer the following questions.
May 68:43 AM
a) What is the maximum height of each blade?
b) Which blade is larger? Determine the radius of each blade.
c) Which blade is spinning faster? Explain.
d) Which blade is set lower? Explain.
6) 3U Modeling Periodic Functions Day 2.notebook
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December 02, 2015
May 68:51 AM
Example 2. Two Cyrus wrecking balls attached to different cranes swing back and forth. The distance the balls move to the left and the right of their resting positions in terms of time can be modelled by the graphs shown.
a) What is the period of each function and what does it represent in this situation?
May 68:53 AM
b) What is the equation of the axis of the curve of each function and what does it represent in the situation?
c) What is the amplitude of each function and what does it represent in this situation?
May 236:40 PM
Example 3. Lydia used a motion detector to measure the horizontal distance between her and a child on a swing. She stood in front of the child and recorded the distance, d(t), in meters over a period of time, t, in seconds. Determine a sinusoidal equation to model this situation.
May 69:03 AM
1 A nail located on the circumference of a water wheel is moving as the current pushes on the wheel. The height of the nail above the water in terms of time can be modelled by the graph shown.
What is the radius of the water wheel?
6) 3U Modeling Periodic Functions Day 2.notebook
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December 02, 2015
May 69:03 AM
2 A nail located on the circumference of a water wheel is moving as the current pushes on the wheel. The height of the nail above the water in terms of time can be modelled by the graph shown.
How far above the water is the axis of the curve?
May 69:03 AM
3 A nail located on the circumference of a water wheel is moving as the current pushes on the wheel. The height of the nail above the water in terms of time can be modelled by the graph shown.
How long does it take for the wheel to rotate?
May 69:00 AM
4 A nail located on the circumference of a water wheel is moving as the current pushes on the wheel. The height of the nail above the water in terms of time can be modelled by the graph shown.
A f(x)=sinxB f(x)=cosxC f(x) = tanx
Which function would be easier to use to model this movement?
May 236:40 PM
Example 4 . A group of students are tracking a friend John, who is riding a Ferris wheel. They know that John reaches the maximum height of 11m at 10s and then reaches the minimum height of 1m at 55s. Use a cosine function to model this movement.
6) 3U Modeling Periodic Functions Day 2.notebook
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December 02, 2015
May 237:13 PM
Example 5. A gymnast is bouncing on a trampoline. When she lands on the trampoline, her feet depress it so that they fall 1m below the level of the deck. When she bounces up, her feet reach a height of 2m above the deck. At her highest point, a stop watch reads 0.6s and at her lowest point it reads 1.8s.
a) Write an equation to represent the distance the gymnast is from the level of the deck at any time.
May 69:18 AM
b) Determine the gymnast's height after 10 seconds.
May 237:13 PM
Example 6. The top of a flagpole sways back and forth in high winds. The top sways 10cm right (+10cm) and 10cm to the left (10cm) of its resting position and moves back and forth 240 times every minute. At t=0 the pole was momentarily at its resting position. Then it starts to moving to the right.
Determine the equation of a sinusoidal function that describes the distance the top of the pole is from its resting position in terms of time.
a)
May 238:10 PM
What are the domain and range for this particular situation?b)
If the wind speed decreases slightly such that the sway of the top of the pole is reduced by 20%, what is the new equation of the sinusoidal function? Assume that the period remains the same.
c)
6) 3U Modeling Periodic Functions Day 2.notebook
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December 02, 2015
May 69:21 AM
Homework:Page 398 #2, 3, 5, 6, 8
