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. a.The height of the tide 30 hours after the original observation is -3.27 feet.b.The height of the tide 30 hours after the original observation is 16 feet.c.The height of the tide 30 hours after the original observation is 8 feet.d.The height of the tide 30 hours after the original observation is -0.63 feet.

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 557088117a.70b.67c.71d.64

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 quarter660.5If you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?

The sine regression model is of the form . Why are sine functions such good models for repetitive behavior?

Consider the following sine regression model Predict the value of y if x equals 30. a. 93.3 b. 85.7 c. 111.7 d. 104.8 Please select the best answer from the choices provided

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.Yes, it shows repeated and periodic behavior. b.Yes, it shows a curve increasing from left to right.c.No, the points are random.d.No, the points depict a parabola.

A sine curve is periodic. What does this mean?a.the curve goes through one cycle and starts overb.there is no patternc.the amplitude stays the samed.one period equals 180 degrees

Choose the graph of the following function: Graph A Graph B Graph C Graph D a. Graph A b. Graph B c. Graph C d. Graph 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). 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. a.Accurate, nothing would help it be more accurate.b.May not be accurate, weather is changing all the time; Information from various states would help make the information more accurate.c.Accurate, it is easily predictable.d.May not be accurate, information was taken over 2 year period; More information from previous years would help the prediction be more accurate.