Pre-Calc Exam Notes 119

Pre-Calc Exam Notes 119 - Properties of Graphs of...

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Properties of Graphs of Trigonometric Functions Section 5.2 119 19. y = 3 sin π x 5 cos π x 20. y =− 5 sin 3 x + 12 cos 3 x 21. y = 2 cos x + 2 sin x 22. Find the amplitude of the function y = 2 sin ( x 2 ) + cos ( x 2 ). For Exercises 23-25, ±nd the period of the given function. Graph one cycle using Gnuplot. 23. y = sin 3 x cos 5 x 24. y = sin x 3 + 2 cos 3 x 4 25. y = 2 sin π x + 3 cos π 3 x 26. Let y = 0.5 sin x sin 12 x . Its graph for x from 0 to 4 π is shown in Figure 5.2.14: -1 -0.5 0 0.5 1 0 π 2 π 3 π 4 π y x 0.5 sin( x ) sin(12 x ) 0.5 sin( x ) 0.5 sin( x ) Figure 5.2.14 Modulated wave y = 0.5 sin x sin 12 x You can think of this function as sin 12 x with a sinusoidally varying “amplitude”of 0.5 sin x . What is the period of this function? From the graph it looks like the amplitude may be 0.5. Without ±nding the exact amplitude, explain why the amplitude is in fact less than 0.5. The function above is known as a modulated wave
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