The Sine Function Answers

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 tide0-0.9825.8347.7867.3482.3310-0.4712-0.21145.32168.83188.31203.8022-0.28240.53Use 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. Then use your model to predict the height of the tide 30 hours after the original observation.

Your sine regression model for a given problem is . Use your model to predict y(95). Round your answer to the nearest hundredth. a. b. c. d. Please select the best answer from the choices provided

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 = 29.882sin(0.887x + 1.271) + 85.635, 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 Tuesday. Round to the nearest customer.DaySunMonTueWedThuFriSatNumber of Customers11679 557088117

Consider the following sine regression model Predict the value of y if x equals 30.

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.DateMoon Phasex: Days since Jan. 8y: The Amount of Moon VisibleJan 8New00Jan 151st quarter70.5Jan 22Full131Jan 30Last quarter220.5Feb 7New300Feb 141st quarter370.5Feb 21Full441Feb 29Last quarter520.5Mar 7New590Mar 141st quarter660.5Using the information above, plot the data points. Does this data indicate that a sine regression may be appropriate in this case? Explain.

A sine curve is periodic. What does this mean?

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

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). Analyze your prediction and explain why your prediction may or may not be accurate. If it might not be accurate, explain what might make the information more accurate.