Table 3 shows the average monthly attendance at LakeNacimiento in California. Find the equation of a trigonometric function to useas a model for this data. (Source: Nacimiento Water Supply Project: Report onRecreational Use at Lake Nacimiento) TABLE 2TABLE 3Phoenix, AZAverage TemperaturesMonthAttendance40,000 -35,000JanJanuaryFebruary546,50030,000Feb586,60025,000Mar62March15,80020,000Apr70April26,00015,000 -May79May38,00010,000 -Jun88June36,0005,000 -Jul9431,300JulyAugustSeptember2 3 4 5 6 7 8 9 10 1 12 1:Aug9223,500Sep8612,000Figure 14Oct75October4,000Nov62November900Dec54December2,100

Answered: TABLE 2 TABLE 3 Phoenix, AZ Average…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Table 3 shows the average monthly attendance at Lake
Nacimiento in California. Find the equation of a trigonometric function to use
as a model for this data. (Source: Nacimiento Water Supply Project: Report on
Recreational Use at Lake Nacimiento)

TABLE 2
TABLE 3
Phoenix, AZ
Average Temperatures
Month
Attendance
40,000 -
35,000
Jan
January
February
54
6,500
30,000
Feb
58
6,600
25,000
Mar
62
March
15,800
20,000
Apr
70
April
26,000
15,000 -
May
79
May
38,000
10,000 -
Jun
88
June
36,000
5,000 -
Jul
94
31,300
July
August
September
2 3 4 5 6 7 8 9 10 1 12 1:
Aug
92
23,500
Sep
86
12,000
Figure 14
Oct
75
October
4,000
Nov
62
November
900
Dec
54
December
2,100

Expert Solution

Step 1

Below graph and table shows the average monthly attendance at Lake Nacimiento in California.

Step 2

Use the cosine function model, $y = k + A \cos (B (x - h))$ .

The amplitude A is the half of the difference between highest point and lowest point.

$\begin{array}{rcl} A & = & \frac{1}{2} (38, 000 - 900) \\ = & 18, 550 \end{array}$

The vertical translation k is the average of highest point and lowest point.

$\begin{array}{rcl} k & = & \frac{1}{2} (38, 000 + 900) \\ = & 19, 450 \end{array}$

The maximum value occur at $x = 5$ and the minimum value occur at $x = 11$ .

The horizonal distance between maximum and minimum values is the half of the period.

Period = $2 (11 - 5) = 12$

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