Trigonometry of Temperatures Worksheet

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I've already provided the average temperature of each month. You will need to graph the points then determine the aspects of the sine or cosine function.Then determine what the function would be for sine and cosine.You can view the file to see further instruction of what to do. Part D is optional I can do it but if you want to you can. I only want to spend up to $10 on this.

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Name Date The Trigonometry of 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 function to write sine and cosine functions that model average monthly temperatures in three different cities. Part A Step 1 Use your favorite search engine or visit your public library to do research to find the latitude of the city in which you live (or the closest major city) and the average monthly temperatures for that city. You will need to cite your source(s). Enter the information in the spaces provided. City Name: Toledo Latitude of the City:41.6528° N Month 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun Average temperatu re 33 f 36 f 47 f 60 f 71 f 81 f month 7 Jul 8 Aug 9 Sep 10 Oct 11 Nov 12 Dec Average temperatu re 85 f 82 f 75 f 63 f 50 f 36 f Sources: https://www.currentresults.com/Weather/Ohio/Places/toledo-temperatures-bymonth-average.php © 2016 Connections Education LLC. All rights reserved. Step 2 Plot the 12 values on a graph. The number corresponding to the month is the first coordinate of each point, and 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 the following values for both a sine function and a cosine function: Sine Cosine Vertical Shift Horizontal Shift Amplitude Period Domain Range Based on the data in your table, write an equation for a sine function and for a cosine function. Sine Function: Cosine Function: Step 3 Choose one of these functions and sketch it on the same graph as the graph with the 12 data points. Write the name of your city as the title for the graph. You will send this graph as an attachment when you submit the portfolio. © 2016 Connections Education LLC. All rights reserved. 2 Part B Repeat steps 1–3 for a new city that is north of the city you used in Part A. Step 1 Choose a city that is north of your city from Part A and find its latitude. Record the average monthly temperatures for that city. You will need to cite your source(s). Enter the information in the spaces provided. Name of Northern City: Detroit Latitude of Northern City: 42.3314° N Month 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun Average 32 f Temperatu re 35 f 46 f 59 f 70 f 79 f Month 7 Jul 8 Aug 9 Sep 10 Oct 11 Nov 12 Dec Average Temperat ure 83 f 81 f 74 f 62 f 49 f 36 f Sources: https://www.currentresults.com/Weather/Michigan/Places/detroit-temperaturesby-month-average.php © 2016 Connections Education LLC. All rights reserved. 3 Step 2 Plot these 12 points on a graph. Use the graph to determine the following values for both a sine function and a cosine function that models the data: Sine Cosine Vertical Shift Horizontal Shift Amplitude Period Domain Range Based on the data in your table, write an equation for a sine function and for a cosine function. Sine Function: Cosine Function: Step 3 Choose one of these functions and sketch it on the same graph as the graph with the 12 data points. Make the title of the graph the name of the city with the word North after the name. You will send this graph as an attachment when you submit the portfolio. © 2016 Connections Education LLC. All rights reserved. 4 Part C Repeat steps 1–3 for a new city that is south of the city you used in Part A. Step 1 Choose a city that is south of your city from Part A and find its latitude. Record the average monthly temperatures for that city. You will need to cite your source(s). Enter the information in the spaces provided. Name of Southern City: Columbus Latitude of Southern City: 39.9612° N Month 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun Average temperatu re 37 f 41 f 51 f 64 f 73 f 82 f Month 7 Jul 8 Aug 9 Sep 10 Oct 11 Nov 12 Dec Average temperatu re 85 f 84 f 77 f 65 f 53 f 40 f Sources © 2016 Connections Education LLC. All rights reserved. 5 Step 2 Plot the 12 values on a graph. Use the graph to determine the following values for both a sine function and a cosine function that models the data: Sine Cosine Vertical Shift Horizontal Shift Amplitude Period Domain Range Based on the data in your table, write an equation for a sine function and for a cosine function. Sine Function: Cosine Function: Step 3 Choose one of these functions and sketch it on the same graph as the graph with the 12 data points. Make the title of the graph the name of the city with the word South after the name. You will send this graph as an attachment when you submit the portfolio. © 2016 Connections Education LLC. All rights reserved. 6 Part D Compare the tables of average temperatures, the equations, and the graphs created for the three cities. How well do your functions fit the data points? What might account for the trigonometric functions not being a perfect fit for the points plotted? Write at least two paragraphs about any conclusions you can draw from the data as shown in each representation. What values were the same in all three tables? What values were different? What might account for these similarities and differences? Be sure to discuss the impact that the latitude of each city has on the trigonometric function that models its monthly temperatures. © 2016 Connections Education LLC. All rights reserved. 7 Part E You will upload the following into the Drop Box: • this completed worksheet • a graph of the average monthly temperatures in your city and the sine or cosine function used to model the data • a graph of the average monthly temperatures in a northern city and the sine or cosine function used to model the data • a graph of the average monthly temperatures in a southern city and the sine or cosine function used to model the data © 2016 Connections Education LLC. All rights reserved. 8
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Explanation & Answer

Here you go! Let me know if you need any edits or have any questions. Hello buddy! I have attached the answer in a word document for you. Also, there is an outline.

Last Name 1

Name
Instructor's name
Course
Date
PRECALCULUS B: The Trigonometry of Temperatures
Part A
Step 1
City Name: Toledo
Latitude of the City:41.6528° N
Table 1: Average monthly temperatures for Toledo City
Month

1
Jan

Average
33
temperature
(°F)

2
Feb

3
Mar

4
Apr

5
May

6
Jun

7
Jul

8
Aug

9
Sep

10
Oct

11
Nov

12
Dec

36

47

60

71

81

85

82

75

63

50

36

Sources: https://www.currentresults.com/Weather/Ohio/Places/toledo-temperatures-bymonth-average.php
Step 2
The plot is shown in the figure below:

Last Name 2

Temperature Plot for Toledo
90
80

Average Temperature, T (°F)

70
60
50
40
30
20
10
0
0

5

10

15

20

25

30

35

Time, t (x10^6 s)

Using the graph to determine the following values for both a sine function and a cosine
function:
Table 2: Sine and a cosine function values
Sine

Cosine

Vertical Shift

59

59

Horizontal Shift (x10^6)

-10.21

-18.144

Amplitude

26

26

Period (x10^6)

62.208

62.208

Domain (x10^6)

[2.592,31.104]

[2.592,31.104]

Range

[33,85]

[33,85]

Based on the data in your table, write an equation for a sine function and for a cosine
function.

Last Name 3

Sine Function:
𝑇 = 𝐴 si n(𝐵(𝑡 + 𝐶)) + 𝐷
2𝜋

Where 𝐴 = 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒; 𝐵 = 𝑝𝑒𝑟𝑖𝑜𝑑 ; 𝐶 = 𝑃ℎ𝑎𝑠𝑒 𝑠ℎ𝑖𝑓𝑡; 𝐷 = 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑠ℎ𝑖𝑓𝑡
Therefore,
𝑇 = 26 si...


Anonymous
Just what I was looking for! Super helpful.

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