Unit 2 Precalculus B - The trigonometry of temperatures Portfolio

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fhcrezna2019

Mathematics

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In this portfolio, you will use your knowledge of the period, amplitude, vertical shift, horizontal shift, domain, and range of a trigonometric functions to write the sine and cosine functions that model average monthly temperatures in the given city.

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Directions: In this portfolio, you will use your knowledge of the period, amplitude, vertical shift, horizontal shift, domain, and range of a trigonometric functions to write the sine and cosine functions that model average monthly temperatures in the given city. Use the data provided below. You do not need to find your own data. 1) 2) Plot the 12 values on a graph. The number corresponding to the month is the first coordinate of each point, and the average temperature for that month is the second coordinate. The points should create a periodic pattern. Assume that the data is, in fact, periodic and use the graph to determine each of the following values for a sine and then a cosine function. You are going to model the data as a sine and cosine function, You can either model it as y = a sin (bt – c) + d or if you prefer y = a sin b(t - c) + d. The c values will be different depending on which approach you use. Start the process by completing the table below based on your graph you created in part 1. Explain how you got these values! Do not just put the values in the table. 3) Based on the data in your table, write an equation for a sine and cosine function You must show your work to earn credit! Do not just fill in values for a, b, c or d. Either show the equation/data you used to get the value or explain clearly in words how you got the values. ***You may not use a regression program to complete this*** Function Coefficient Sine Function Cosine Function y= a sine (bt - c) + d y= a cos (bt - c) + d y = a sine b(t - c) + d y = a cos b(t - c) + d a b c d 4) Now put it together and write your sine and cosine functions! 5) Let’s see how well it fits. a) Create a plot of your original data from step 1 and a graph of your sine function. b) Create a plot of your original data from step 1 and a graph of your cosine function. 6) Comment on how well the functions model the data. 7) Extra Credit - What parameters (vertical shift, horizontal shift, amplitude, period, domain and range) changed when you modeled it with a cosine function instead of a sine function? Why did these change? Do you think one is more advantageous than the other? In order to earn the full extra credit please be specific in your answers
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The trigonometric of the temperatures
PRECALCULUS B
Directions: In this portfolio, you will use your knowledge of the period, amplitude,
vertical shift, horizontal shift, domain, and range of a trigonometric functions to write
the sine and cosine functions that model average monthly temperatures in the given
city. Use the data provided below. You do not need to find your own data.
1) Plot the 12 values on a graph. The number corresponding to the month is the first
coordinate of each point, and the average temperature for that month is the second
coordinate. The points should create a periodic pattern. Assume that the data is, in
fact, periodic and use the graph to determine each of the following values for a sine
and then a cosine function.
City name: Eden Prairie
Latitude of the city: 44.8547°
Month

1
Jan

Average
Temperature 15.5°

Month

7
Jul

Average
Temperature 73.5°
Solution:

2
Feb
20°

8
Aug
71°

3
Mar
32.5°

9
Sep
61.5°

4
Apr
47°

10
Oct
48.5°

5
May
59.5°

11
Nov
33.5°

6
Jun
69°

12
Dec
19.5°

Tempersture (°)

Month vs Temperature
80
70
60
50
40
30
20
10
0
0

2

4

6

8

10

12

14

Month

2) You are going to model the data as a sine and cosine function, You can either
model it as y = a sin (bt – c) + d or if you prefer y = a sin b(t - c) + d. The c values
will be different depending on which approach you use. Start the process by
completing the table below based on your graph you created in part 1. Explain how
you got these values! Do not just put the values in the table.

Sine

Cosine

44.5

44.5

Horizontal shift

4

7

Amplitude

29

29

Period

12

12

Domain

(−∞, ∞)

(−∞, ∞)

(15.5,73.5)

(15.5,73.5)

Vertical Shift

Range

|𝐴| =

1
(𝑀𝑎𝑥 − 𝑀𝑖𝑛)
2

But, we know that
𝑀𝑎𝑥 = 73.5° and 𝑀𝑖𝑛 = 15.5°
Now, substitut...


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I was struggling with this subject, and this helped me a ton!

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