The visitors’ guide to St. Petersburg, Florida, contains the chart shown in Figure 1.77 to advertise their good weather. Fit a trigonometric function approximately to the data, where H is temperature in degrees Fahrenheit, and the independent variable is time in months. In order to do this, you will need to estimate the amplitude and period of the data, and when the maximum occurs. (There are many possible answers to this problem, depending on how you read the graph.) Figure 1.77: “St. Petersburg...where we’re famous for our wonderful weather and year-round sunshine.” (Reprinted with permission)
The visitors’ guide to St. Petersburg, Florida, contains the chart shown in Figure 1.77 to advertise their good weather. Fit a trigonometric function approximately to the data, where H is temperature in degrees Fahrenheit, and the independent variable is time in months. In order to do this, you will need to estimate the amplitude and period of the data, and when the maximum occurs. (There are many possible answers to this problem, depending on how you read the graph.) Figure 1.77: “St. Petersburg...where we’re famous for our wonderful weather and year-round sunshine.” (Reprinted with permission)
The visitors’ guide to St. Petersburg, Florida, contains the chart shown in Figure 1.77 to advertise their good weather. Fit a trigonometric function approximately to the data, where H is temperature in degrees Fahrenheit, and the independent variable is time in months. In order to do this, you will need to estimate the amplitude and period of the data, and when the maximum occurs. (There are many possible answers to this problem, depending on how you read the graph.)
Figure 1.77: “St. Petersburg...where we’re famous for our wonderful weather and year-round sunshine.” (Reprinted with permission)
In whoville, the amount of rainfall varies greatly each week and follows a sinusoidal pattern. The following data is the recorded millimeters (mm) of precipitation across 14 weeks. Determine a sine and a cosine function that approximates the amount of rainfall over time in weeks. Decimals are allowed.
Week 1, rainfall(mm) - 1.4
Week 2, rainfall(mm) - 3.1
Week 3, rainfall(mm) - 4.3
Week 4, rainfall(mm) - 2.9
Week 5, rainfall(mm) - 1.2
Week 6, rainfall(mm) - 0.1
Week 7, rainfall(mm) - 1.3
Week 8, rainfall(mm) - 2.7
Week 9, rainfall(mm) - 4.3
Week 10, rainfall(mm) - 3.2
Week 11, rainfall(mm) - 1.1
Week 12, rainfall(mm) - 0.2
Week 13, rainfall(mm) - 1.2
Week 14, rainfall(mm) - 2.8
A bus hits a bump in the road, raising the back row seats by 16 inches above their regular
position of two feet above the road surface. The seats then continue to bounce up and down for
a few seconds, with each bounce lasting a full second.
A. Use the information above to give a trigonometric model for the height of the seats
above the road, as a function of the time since the peak of the first bump.
B. Due to the hard-working shock absorbers in the bus, each bounce is less severe than
the one before. The table below gives the height above the usual seat position for the
first three bounces.
1
16
Show that the data in this table can represent an exponential function and use the table
to give an exponential function for the amplitude of the bounce as a function of time.
C. Combine the functions from parts (a) and (b) so that the exponential function is
substituted for the amplitude in the trigonometric model. Use this function to find how
long it will take for the peak of each bounce to…
If you were tasked with collecting data that could follow a trigonometric function, describe your procedure here:
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY