What Function Models Yearly Sunrise Times in New York?

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Homework Help Overview

The original poster presents a problem involving the modeling of yearly sunrise times in New York using a function. They have been given a dataset that includes week numbers and corresponding sunrise times expressed in hours and minutes.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of using a periodic function, such as sine or cosine, to model the data. There are suggestions to convert the time format for better fitting with trigonometric functions. Some participants propose plotting the data to visualize the trends.

Discussion Status

There is an ongoing exploration of different methods to analyze the data, including converting time formats and considering the use of trigonometric functions. Some participants have shared their calculations and insights, but no consensus has been reached on a specific approach yet.

Contextual Notes

The original poster mentions that the problem was assigned without clear guidance, which may contribute to the varied approaches being discussed. There is also a note about the potential confusion regarding the decimal notation of time.

jballer23
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1. I was given times for the sunrise in new york for one year. The question was that I needed to find a function that would best represent the data. The first column is the week number and the second is the time in hours and min.
1 7.2
2 7.2
3 7.18
4 7.14
5 7.09
6 7.02
7 6.54
8 6.45
9 6.35
10 6.24
11 6.13
12 6.01
13 5.5
14 5.38
15 5.27
16 5.16
17 5.06
18 4.56
19 4.47
20 4.4
21 4.34
22 4.29
23 4.26
24 4.24
25 4.26
26 4.29
27 4.33
28 4.38
29 4.44
30 4.5
31 4.57
32 5.04
33 5.11
34 5.17
35 5.24
36 5.31
37 5.38
38 5.45
39 5.52
40 5.59
41 6.06
42 6.14
43 6.22
44 6.3
45 6.39
46 6.47
47 6.55
48 7.02
49 7.08
50 7.14
51 7.18
52 7.18



2. I'm not sure what my teacher was thinking on this problem she just asked us to take it home and figure it out anyway that we could.



3. I've tried using my graphing calculator to find a line of best fit but none of them worked all too well. I think that its got to be a periodic function because it would repeat farly close to the same time the next year. So I was thinking maybe a sin or cos fuction. I'm not sure. If you could help that would be more helpful than you could imagine
 
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Don't get confused by the decimal notation: they're still times.
For example, 7.20 is actually 20 minutes past 7, so that's 7 and 1/3 hours after midnight. If you convert all the numbers in this way (7.2 -> 7.333, 6.14 -> 6.23333, etc) you will indeed get an almost perfect fit for a trig function.
 
wouldn't plotting the actual graph help??
 
this has an attached to it. Maybe that will help
 

Attachments

Did you look at my suggestion yet?
Then I get the list
Code: 
1	7.333333333333334
2	7.333333333333334
3	7.3
4	7.2333333333333325
5	7.1499999999999995
6	7.033333333333332
7	6.9
8	6.75
9	6.583333333333333
10	6.4
11	6.216666666666667
12	6.016666666666667
13	5.833333333333333
14	5.633333333333333
15	5.449999999999999
16	5.266666666666667
17	5.1
18	4.933333333333333
19	4.783333333333333
20	4.666666666666667
21	4.566666666666666
22	4.483333333333333
23	4.433333333333333
24	4.4
25	4.433333333333333
26	4.483333333333333
27	4.55
28	4.633333333333333
29	4.733333333333334
30	4.833333333333333
31	4.95
32	5.066666666666666
33	5.183333333333334
34	5.283333333333333
35	5.4
36	5.516666666666666
37	5.633333333333333
38	5.75
39	5.866666666666666
40	5.983333333333333
41	6.1
42	6.2333333333333325
43	6.366666666666666
44	6.5
45	6.6499999999999995
46	6.783333333333333
47	6.916666666666666
48	7.033333333333332
49	7.133333333333334
50	7.2333333333333325
51	7.3
52	7.3
and you shouldn't have too much trouble throwing in a cosine.