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4.4 – Graphing Sine and Cosine Functions APPLICATIONS

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Ex. 1 Use the table below to write a sinusoidal function that models the number of hours of daylight for New York City as a function of time x, where x = 1 represents Jan. 15, x = 2 represents Feb. 15, and so on. Then use your model to estimate the number of hours of daylight on Sept. 30. MonthHrs. DaylightMonthHrs. Daylight Jan.9.58July14.8 Feb.10.67Aug.13.8 Mar.11.9Sept.12.48 Apr.13.3Oct.11.15 May14.43Nov.9.9 June15.07Dec.9.27

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1.Make a scatter plot on your graphing calc.

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STAT, EDIT, enter months 1-12 for L1 and the hours for L2.

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window.

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot.

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot. 2 nd, Y=, ENTER, ENTER (to turn on), GRAPH

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot. 2 nd, Y=, ENTER, ENTER (to turn on), GRAPH 4.Calculate the regression equation.

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot. 2 nd, Y=, ENTER, ENTER (to turn on), GRAPH 4.Calculate the regression equation. STAT, >CALC, C:SinReg, ENTER

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot. 2 nd, Y=, ENTER, ENTER (to turn on), GRAPH 4.Calculate the regression equation. STAT, >CALC, C:SinReg, ENTER ***Write the reg eq.

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1.Make a scatter plot on your graphing calc. STAT, EDIT, enter months 1-12 for L1 and the hours for L2. 2.Change your window. WINDOW, Xmin = 0, Xmax = 12, Xscl = 1, Ymin = 0, Ymax = 15.5, Yscl = 0.5, Xres = 1 3.Graph the scatter plot. 2 nd, Y=, ENTER, ENTER (to turn on), GRAPH 4.Calculate the regression equation. STAT, >CALC, C:SinReg, ENTER ***Write the reg eq. y = 2.9sin(0.5x-1.6)+12.1

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5.Graph Reg. Eq.

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Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH

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5.Graph Reg. Eq. Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH 6.Calculate needed value.

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5.Graph Reg. Eq. Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH 6.Calculate needed value. Since Sept. 15 would be when x = 9 and Oct. 15 would be when x = 10, Sept. 30 will be when x = 9.5.

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5.Graph Reg. Eq. Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH 6.Calculate needed value. Since Sept. 15 would be when x = 9 and Oct. 15 would be when x = 10, Sept. 30 will be when x = 9.5. 2 nd, CALC, 1:value, 9.5, ENTER

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5.Graph Reg. Eq. Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH 6.Calculate needed value. Since Sept. 15 would be when x = 9 and Oct. 15 would be when x = 10, Sept. 30 will be when x = 9.5. 2 nd, CALC, 1:value, 9.5, ENTER ***Write down this answer.

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5.Graph Reg. Eq. Y=, VARS, 5:Statistics, >>EQ, 1:RegEQ, GRAPH 6.Calculate needed value. Since Sept. 15 would be when x = 9 and Oct. 15 would be when x = 10, Sept. 30 will be when x = 9.5. 2 nd, CALC, 1:value, 9.5, ENTER ***Write down this answer. On Sept. 30 there will be approximately 11.8 hours of daylight in New York City.

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