460 CHAPTER 6 Trigonometric Functions (a) Draw a scatter plot of the data for one period. (b) Find a sinusoidal function of the form ω φ ( ) = − + y A x B sin that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter plot of the data. 31. Monthly Temperature The following data represent the average monthly temperatures for Indianapolis, Indiana. January, 1 February, 2 March, 3 April, 4 May, 5 June, 6 July, 7 August, 8 September, 9 October, 10 November, 11 December, 12 28.1 32.1 42.2 53.0 62.7 72.0 75.4 74.2 66.9 55.0 43.6 31.6 Source: U.S. National Oceanic & Atmospheric Administration Month, x Average Monthly Temperature, y (°F) (a) Draw a scatter plot of the data for one period. (b) Find a sinusoidal function of the form ω φ ( ) = − + y A x B sin that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter plot of the data. 32. Monthly Temperature The data on the next page represent the average monthly temperatures for Baltimore, Maryland. (a) Draw a scatter plot of the data for one period. (b) Find a sinusoidal function of the form ω φ ( ) = − + y A x B sin that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter plot of the data. 29. Hurricanes Hurricanes are categorized using the SaffirSimpson 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 data below represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2020. Decade, x Major Hurricanes, H 1921–1930, 1 17 1931–1940, 2 16 1941–1950, 3 29 1951–1960, 4 33 1961–1970, 5 27 1971–1980, 6 16 1981–1990, 7 16 1991–2000, 8 27 2001–2010, 9 33 2011–2020, 10 29 Source: U.S. National Oceanic & Atmospheric Administration (a) Draw a scatter plot of the data. (b) Find a sinusoidal function of the form ω φ ( ) = − + y A x B sin that models the data. (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter plot of the data. 30. Monthly Temperature The following data represent the average monthly temperatures for Washington, D.C. January, 1 February, 2 March, 3 April, 4 May, 5 June, 6 July, 7 August, 8 September, 9 October, 10 November, 11 December, 12 36.0 39.0 46.8 56.8 66.0 75.2 79.8 78.1 71.0 59.5 49.6 39.7 Source: U.S. National Oceanic & Atmospheric Administration Month, x Average Monthly Temperature, y (°F)
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