Average Monthly Temperature The average monthly temperature (in °F) in San Antonio, Texas, can be modeled by the function TT f (x) = 16.5 sin (x – 4) | + 68.5, 6. where x is the month, with x = 1 corresponding to January, x = 2 corresponding to February, and so on. (Data from National Climatic Data Center.) (a) Graph f in the window [0, 25] by [40, 90]. (b) Determine the amplitude, period, phase shift, and vertical translation of f. (c) What is the average monthly temperature for the month of December?
Average Monthly Temperature The average monthly temperature (in °F) in San Antonio, Texas, can be modeled by the function TT f (x) = 16.5 sin (x – 4) | + 68.5, 6. where x is the month, with x = 1 corresponding to January, x = 2 corresponding to February, and so on. (Data from National Climatic Data Center.) (a) Graph f in the window [0, 25] by [40, 90]. (b) Determine the amplitude, period, phase shift, and vertical translation of f. (c) What is the average monthly temperature for the month of December?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 67E
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Average Monthly Temperature
Answer (a) through (e). Show your work.
![Average Monthly Temperature The average monthly temperature (in °F) in San
Antonio, Texas, can be modeled by the function
TT
f(x) = 16.5 sin
(x
+ 68.5,
where x is the month, with x = 1 corresponding to January, x = 2 corresponding to
February, and so on. (Data from National Climatic Data Center.)
(a) Graph f in the window [0, 25] by [40, 90].
(b) Determine the amplitude, period, phase shift, and vertical translation of f.
(c) What is the average monthly temperature for the month of December?
(d) Determine the minimum and maximum average monthly temperatures and the
months when they occur.
(e) What would be an approximation for the average annual temperature in San
Antonio? How is this related to the vertical translation of the sine function in the
formula for f?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597a178-4b94-4d11-82bd-885a4bd2a85c%2F13247316-9827-4819-a702-792cf15a03c2%2Frd12y4b_processed.png&w=3840&q=75)
Transcribed Image Text:Average Monthly Temperature The average monthly temperature (in °F) in San
Antonio, Texas, can be modeled by the function
TT
f(x) = 16.5 sin
(x
+ 68.5,
where x is the month, with x = 1 corresponding to January, x = 2 corresponding to
February, and so on. (Data from National Climatic Data Center.)
(a) Graph f in the window [0, 25] by [40, 90].
(b) Determine the amplitude, period, phase shift, and vertical translation of f.
(c) What is the average monthly temperature for the month of December?
(d) Determine the minimum and maximum average monthly temperatures and the
months when they occur.
(e) What would be an approximation for the average annual temperature in San
Antonio? How is this related to the vertical translation of the sine function in the
formula for f?
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