The Sine Function Answers

In a basic sine curve, where can the zeros NOT be found?

Choose the graph of the following function: Graph A Graph B Graph C Graph D

The tide is the regular rising or falling of the ocean’s surface. This is due in large part to the gravitational forces of the moon. The following table represents water level of the tide off the coast of Kings Point, N.Y., for a 24 hour period, February 9th through February 10th of 2009.HourMeasurement in feet above the average low tide0-0.9825.8347.7867.3482.3310-0.4712-0.21145.32168.83188.31203.8022-0.28240.53Plot the data points given in the table using hour as the independent variable. Does this data indicate that a sine regression may be appropriate in this case? Explain.

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table: Month Average Maximum Monthly Temperature Jan 48.1 Feb 50.9 Mar 62.4 Apr 67.0 May 76.5 Jun 83.9 Jul 86.8 Aug 88.1 Sep 79.2 Oct 69.9 Nov 59.5 Dec 49.6 Let x represent the months and y represent the average maximum monthly temperature. Plot the data on a scatterplot. Choose the plot that best represents the data. a. b. c. d. Please select the best answer from the choices provided

Interpret the following sine regression model. What is the value of d in this equation?

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table: Month Average Maximum Monthly Temperature Jan 48.1 Feb 50.9 Mar 62.4 Apr 67.0 May 76.5 Jun 83.9 Jul 86.8 Aug 88.1 Sep 79.2 Oct 69.9 Nov 59.5 Dec 49.6 Plot the data on a scatter plot. Produce a sine regression model for the data. Round the values for a, b, c, and d to the nearest 0.001. a. b. c. d. Please select the best answer from the choices provided

The tide is the regular rising or falling of the ocean’s surface. This is due in large part to the gravitational forces of the moon. The following table represents water level of the tide off the coast of Kings Point, N.Y., for a 24 hour period, February 9th through February 10th of 2009. Hour Measurement in feet above the average low tide 0 -0.98 2 5.83 4 7.78 6 7.34 8 2.33 10 -0.47 12 -0.21 14 5.32 16 8.83 18 8.31 20 3.80 22 -0.28 24 0.53 Use your graphing calculator to produce a sine regression model for the data in the table. Round a, b, c, and d to the nearest 0.001. a. b. c. d. Please select the best answer from the choices provided

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:MonthAverage Maximum Monthly TemperatureJan48.1Feb50.9Mar62.4Apr67.0May76.5Jun83.9Jul86.8Aug88.1Sep79.2Oct69.9Nov59.5Dec49.6Plot the data on a scatter plot. Produce a sine regression model for the data. Round the values for a, b, c, and d to the nearest 0.001. Using the sine regression model predict what the temperature would be given y(30).

Interpret the following sine regression model. What is the value of c in this equation?

The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible. The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008. Date Moon Phase x: Days since Jan. 8 y: The Amount of Moon Visible Jan 8 New 0 0 Jan 15 1st quarter 7 0.5 Jan 22 Full 13 1 Jan 30 Last quarter 22 0.5 Feb 7 New 30 0 Feb 14 1st quarter 37 0.5 Feb 21 Full 44 1 Feb 29 Last quarter 52 0.5 Mar 7 New 59 0 Mar 14 1st quarter 66 0.5 Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. a. b. c. d. Please select the best answer from the choices provided

Consider the following sine regression model Predict y(14).

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table: Month Average Maximum Monthly Temperature Jan 48.1 Feb 50.9 Mar 62.4 Apr 67.0 May 76.5 Jun 83.9 Jul 86.8 Aug 88.1 Sep 79.2 Oct 69.9 Nov 59.5 Dec 49.6 To get a feel for the relationship between the month and the average high temperatures, the data is plotted on the following scatter plot. If the plot was extended to a two year period with 1 = Jan of the first year, 12 = Dec of the first year, 13 = Jan of the second year, 24 = Dec of the second year, describe the plot with the additional information.

The average number of customers per day at a home improvement store is given in the following table. The sine regression equation was found to be y = 33.690sin(0.887x + 1.337) + 81.684, where x represents the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use this model to predict the average number of customers on Thursday. Round to the nearest customer.DaySunMonTueWedThuFriSatNumber of Customers114756051 86118

Interpret the following sine regression model. What is the value of b in this equation?

Choose the graph of the following function: Graph A Graph B Graph C Graph D

The average number of customers per day at a home improvement store is given in the following table. Let x represent the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use a graphing calculator to produce a sine regression model for the data. Round a, b, c, and d to the nearest thousandth.DaySunMonTueWedThuFriSatNumber of Customers1157760516886120

Interpret the following sine regression model. What is the value of a in this equation?