Monthly Temperature The following data represent the

For the graph of , the number is called the . f v y = A sin1vx - f2

True or False Only two data points are required by a graphing utility to find the sine function of best fit.

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 4 sin12x - p2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 3 sin13x - p2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 2 cosa3x + p 2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 3 cos12x + p2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = -3 sina2x + b p 2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = -2 cosa2x - p 2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 4 sin 1px + 22 - 5

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 2 cos12px + 42 + 4

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 3 cos1px - 22 + 5

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 2 cos12px - 42 - 1

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = - 3 sina -2x + b p 2

In Problems 314, find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = -3 cosa -2x + p 2

In Problems 1518, write the equation of a sine function that has the given characteristicsAmplitude: 2 Period: Phase shift:

In Problems 1518, write the equation of a sine function that has the given characteristicsAmplitude: 3 Period: Phase shift: 2

In Problems 1518, write the equation of a sine function that has the given characteristicsAmplitude: 3 Period: Phase shift

In Problems 1518, write the equation of a sine function that has the given characteristicsAmplitude: 2 Period: Phase shift: -2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = 2 tan14x - p2y = 2 tan14x - p2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = b 12cot12x - p2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = 3 csca2x - sec13x - p2 p 4

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = 1 2 y = 3 csca2x - sec13x - p2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = -cota2x + b p 2 b

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = -tana3x + y = -sec12px + p2 b p 2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = -sec12px + p2

In Problems 1926, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periodsy = -csca - 1 2 px + p 4 y = -tana3x + y = -sec12px + p2 b

Alternating Current (ac) Circuits The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods.I1t2 = 120 sina30pt - p 3 b t 0

Alternating Current (ac) Circuits The current I, in amperes, flowing through an ac (alternating current) circuit at time t, in seconds, is What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods.I1t2 = 220 sina60pt - p 6 b t 0

Monthly Temperature The following data represent the average monthly temperatures for Juneau,Alaska.(a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form 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) Draw the sinusoidal function of best fit on a scatter diagram of the data.

Monthly Temperature The following data represent the average monthly temperatures for Washington, D.C. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form 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.

Monthly Temperature The following data represent the average monthly temperatures for Indianapolis, Indiana.(a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form 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.

Monthly Temperature The following data represent the average monthly temperatures for Baltimore, Maryland. (a) Draw a scatter diagram of the data for one period. (b) Find a sinusoidal function of the form 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.

Tides The length of time between consecutive high tides is 12 hours and 25 minutes.According to the National Oceanic and Atmospheric Administration, on Saturday, July 25, 2009, in Charleston, South Carolina, high tide occurred at 11:30 AM (11.5 hours) and low tide occurred at 5:31 PM (17.5167 hours).Water heights are measured as the amounts above or below the mean lower low water.The height of the water at high tide was 5.84 feet, and the height of the water at low tide was -0.37 foot. (a) Approximately when will the next high tide occur? (b) Find a sinusoidal function of the form that models the data. (c) Use the function found in part (b) to predict the height of the water at 3 PM on July 25, 2009.

Tides The length of time between consecutive high tides is 12 hours and 25 minutes.According to the National Oceanic and Atmospheric Administration, on Saturday, July 25, 2009, in Sitka Sound, Alaska, high tide occurred at 2:37 AM (2.6167 hours) and low tide occurred at 9:12 PM (9.2 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 11.09 feet, and the height of the water at low tide was -2.49 feet.(a) Approximately when will the next high tide occur? (b) Find a sinusoidal function of the form that models the data. (c) Use the function found in part (b) to predict the height of the water at 6 PM.

Hours of Daylight According to the Old Farmers Almanac, in Miami, Florida, the number of hours of sunlight on the summer solstice of 2010 was 13.75, and the number of hours of sunlight on the winter solstice was 10.55. (a) Find a sinusoidal function of the form that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part (a). (d) Look up the number of hours of sunlight for April 1 in the Old Farmers Almanac, and compare the actual hours of daylight to the results found in part (c).

Hours of Daylight According to the Old Farmers Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice of 2010 was 15.30, and the number of hours of sunlight on the winter solstice was 9.10. (a) Find a sinusoidal function of the form that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part (a).(d) Look up the number of hours of sunlight for April 1 in the Old Farmers Almanac, and compare the actual hours of daylight to the results found in part (c).

Hours of Daylight According to the Old Farmers Almanac, in Anchorage, Alaska, the number of hours of sunlight on the summer solstice of 2010 was 19.42 and the number of hours of sunlight on the winter solstice was 5.48. (a) Find a sinusoidal function of the form that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part (a). *(d) Look up the number of hours of sunlight for April 1 in the Old Farmers Almanac, and compare the actual hours of daylight to the results found in part (c).

Hours of Daylight According to the Old Farmers Almanac, in Honolulu, Hawaii, the number of hours of sunlight on the summer solstice of 2010 was 13.43 and the number of hours of sunlight on the winter solstice was 10.85. (a) Find a sinusoidal function of the form that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April 1, the 91st day of the year. (c) Draw a graph of the function found in part (a). (d) Look up the number of hours of sunlight for April 1 in the Old Farmers Almanac, and compare the actual hours of daylight to the results found in part (c).

Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis.

Find an application in your major field that leads to a sinusoidal graph.Write a paper about your findings.