SECTION 6.6 Phase Shift; Sinusoidal Curve Fitting 459 The sinusoidal function of best fit is ( ) = − + y x 21.54 sin 0.56 2.44 51.77 where x represents the month and y represents the average monthly temperature. Figure 91 shows the graph of the sinusoidal function of best fit on the scatter plot, using a TI-84 Plus CE. Figure 92 shows the result using Desmos. Now Work PROBLEMS 2 9 (d) AND (e) Concepts and Vocabulary 6.6 Assess Your Understanding 1. For the graph of ω φ ( ) = − y A x sin , the number φ ω is called the . 2. True or False A graphing utility requires only two data points to find the sine function of best fit. Skill Building In Problems 3–22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. 3. π ( ) = − y x 4 sin 2 4. π ( ) = − y x 3sin 3 5. π ( ) = + y x 2 cos 3 2 6. π ( ) = + y x 3cos 2 7. π ( ) = − + y x 3sin 2 2 8. π ( ) = − − y x 2 cos 2 2 9. π ( ) = + − y x 4cos 4 2 10. π ( ) = + + y x 5sin 4 3 11. π( ) = + − y x 4 sin 2 5 12. π ( ) = + + y x 2cos 2 4 4 13. π( ) = − + y x 3cos 2 5 14. π ( ) = − − y x 2 sin 2 4 1 15. π ( ) = − − + y x 3sin 2 2 16. π ( ) = − − + y x 3cos 2 2 17. π ( ) = − y x 2 tan 4 18. π ( ) = − y x 1 2 cot 2 19. π ( ) = − y x 3csc 2 4 20. π ( ) = − y x 1 2 sec 3 21. π ( ) = − − − + y x 2cos 4 1 22. π ( ) = − − − − y x 2 sin 4 2 2 In Problems 23–26, write an equation of a sine function that has the given characteristics. Applications and Extensions 27. Alternating Current (AC) Circuits The current I , in amperes, flowing through an AC (alternating current) circuit at time t , in seconds, is π π ( ) ( ) = − ≥ I t t t 120 sin 30 3 0 What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods. 28. Alternating Current (AC) Circuits The current I , in amperes, flowing through an AC (alternating current) circuit at time t , in seconds, is π π ( ) ( ) = − ≥ I t t t 220 sin 60 6 0 What is the period? What is the amplitude? What is the phase shift? Graph this function over two periods. 23. Amplitude: 2 Period: π Phase shift: 1 2 24. Amplitude: 3 Period: 2 π Phase shift: 2 25. Amplitude: 3 Period: 3π Phase shift: 1 3 − 26. Amplitude: 2 Period: π Phase shift: 2− 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure Figure 91 75 0 13 25 Figure 92 Figure 90
RkJQdWJsaXNoZXIy NjM5ODQ=