Hurricanes Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111-130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The following data represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010. (a) Draw a scatter diagram of the data. (b) Find a sinusoidal function of the form y = A sin ( ω x − ϕ ) + B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.
Hurricanes Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111-130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The following data represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010. (a) Draw a scatter diagram of the data. (b) Find a sinusoidal function of the form y = A sin ( ω x − ϕ ) + B that models the data. (c) Draw the sinusoidal function found in part ( b ) on the scatter diagram. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter diagram of the data.
Solution Summary: The author explains how to find a sinusoidal function of the form y = A sin + B that models the data.
Hurricanes
Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111-130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The following data represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.
(a) Draw a scatter diagram of the data.
(b) Find a sinusoidal function of the form
that models the data.
(c) Draw the sinusoidal function found in part
on the scatter diagram.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter diagram of the data.
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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