## Description

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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## Explanation & Answer

Here is my answer :)

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...