1. 4.4 – Graphing Sine and Cosine Functions APPLICATIONS

2. 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

3. 1.Make a scatter plot on your graphing calc.

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

5. 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.

6. 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

7. 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.

8. 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

9. 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.

10. 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

11. 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.

12. 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

13. 5.Graph Reg. Eq.

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

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

16. 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.

17. 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

18. 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.

19. 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.