Download - 11B Topic 4_2
![Page 1: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/1.jpg)
11B Topic 4_2
![Page 2: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/2.jpg)
6. Applications of periodic functions
![Page 3: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/3.jpg)
Challenge Question (1)
High tide is 4.5 m at midnightLow tide is 0.5m at 6am
i) Find the height of the tide at 7pm?ii) Between what times will the tide be greater
than or equal to 3m?
![Page 4: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/4.jpg)
Use y = A cos B(x+C) + D
i) Find “A”
Tide range = 4.5 - 0.5 = 4 A = 2 y = 2cos B(x+C) + D
iii) Find “B”
Period = 12
ii) Find “D”
D = 4.5 – 2 = 2.5
y = 2cos B(x+C) + 2.5
2Period=
212
6
2cos 2.56
B
B
B
y x C
iv) Find “C”
We can see from the graph that no C-value is needed
High tide is 4.5 m at midnight Low tide is 0.5m at 6ami) Find the height of the tide at 7pm?ii) Between what times will the tide be greater than or equal
to 3m?
2cos 2.56xy
![Page 5: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/5.jpg)
2cos 2.56xy
By use of TI calculator…
i) What is the tide height at 7pm?
• Graph using suitable windows• 2nd Calc option 1. Value• Enter 19• Answer = 0.77m (2D.P.)
ii) Tide above 3m• Add y = 3 to the graph• 2nd Calc option 5.
Intersect• Follow prompts• Answer = • MN – 2:31am • 9:29am – 2:31pm• 9:29pm – MN
![Page 6: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/6.jpg)
Challenge Question (2)
High tide of 4.2m occurs in a harbor at 4am Tuesday and the following low tide of 0.8m occurs 6¼ hours later. If a ship entering the harbor needs a minimum depth of water of 3m, what times on Tuesday can this vessel enter?
![Page 7: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/7.jpg)
Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time:
(a) Find the period and amplitude of the movement.(b) Predict the displacement at 10 seconds.(c) Find all the times up to 20 sec when the displacement will be 5 cm to the
right (shown as positive on the graph)
X
Y
1 2 3 4 5
-8-6-4-2
2468
0
![Page 8: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/8.jpg)
Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time:
(a) Find the period and amplitude of the movement.(b) Predict the displacement at 10 seconds.(c) Find all the times up to 20 sec when the displacement will be 5 cm to the
right (shown as positive on the graph)
X
Y
1 2 3 4 5
-8-6-4-2
2468
0
Period = 4.5 - 0.5
= 4 sec
![Page 9: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/9.jpg)
Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time:
(a) Find the period and amplitude of the movement.(b) Predict the displacement at 10 seconds.(c) Find all the times up to 20 sec when the displacement will be 5 cm to the
right (shown as positive on the graph)
X
Y
1 2 3 4 5
-8-6-4-2
2468
0
Amplitude = 8
![Page 10: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/10.jpg)
Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time:
(a) Find the period and amplitude of the movement.(b) Predict the displacement at 10 seconds.(c) Find all the times up to 20 sec when the displacement will be 5 cm to the
right (shown as positive on the graph)
X
Y
1 2 3 4 5
-8-6-4-2
2468
0
Since the period = 4 sec
Displacement after 10 sec will be the same as displacement after 2 sec
= 5.7cm to the left
![Page 11: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/11.jpg)
Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time:
(a) Find the period and amplitude of the movement.(b) Predict the displacement at 10 seconds.(c) Find all the times up to 20 sec when the displacement will be 5 cm to the
right (shown as positive on the graph)
X
Y
1 2 3 4 5
-8-6-4-2
2468
0
Displacement= 5cm
t = 1.1
3.9 7.9, 11.9, 15.9, 19.9
5.1, 9.1, 13.1, 17.1
![Page 12: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/12.jpg)
Exercise
NewQ P 179 Set 5.2 1,3
![Page 13: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/13.jpg)
Model: Find the equation of the curve below.
X
Y
1 2 3 4 5 6 7 8 9 10
-2
2
0
Amplitude = 2.5 y = a sin b(x+c)
![Page 14: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/14.jpg)
Model: Find the equation of the curve below.
X
Y
1 2 3 4 5 6 7 8 9 10
-2
2
0
Amplitude = 2.5 y = 2.5 sin b(x+c)
Period = 6
Period = 2/b 6 = 2/b
b = /3
![Page 15: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/15.jpg)
Model: Find the equation of the curve below.
X
Y
1 2 3 4 5 6 7 8 9 10
-2
2
0
Amplitude = 2.5 y = 2.5 sin /3(x+c)
Period = 6
Period = 2/b 6 = 2/b
b = /3
Phase shift = 4 ()
so c = -4
![Page 16: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/16.jpg)
Model: Find the equation of the curve below.
X
Y
1 2 3 4 5 6 7 8 9 10
-2
2
0
Amplitude = 2.5 y = 2.5 sin /3(x-4)
Period = 6
Period = 2/b 6 = 2/b
b = /3
Phase shift = 4 ()
so c = -4
![Page 17: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/17.jpg)
Exercise
NewQ P 183 Set 5.3 1,4
![Page 18: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/18.jpg)
Exercise 5.3 pg 183, No.4
![Page 19: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/19.jpg)
![Page 20: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/20.jpg)
![Page 21: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/21.jpg)
![Page 22: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/22.jpg)
![Page 23: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/23.jpg)
![Page 24: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/24.jpg)
![Page 25: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/25.jpg)
![Page 26: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/26.jpg)
![Page 27: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/27.jpg)
![Page 28: 11B Topic 4_2](https://reader030.vdocuments.us/reader030/viewer/2022033022/56815b9c550346895dc9a2f7/html5/thumbnails/28.jpg)
Find the equation of the curve below in terms of the sin function and the cosine
function.