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Homework, Page 392

Homework, Page 392. Find the amplitude of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x . 1. y = 2 sin x

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Homework, Page 392

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  1. Homework, Page 392 Find the amplitude of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. 1. y = 2 sin x The graph of y = 2 sin x may be obtained from the graph of y = sin x by applying a vertical stretch of 2.

  2. Homework, Page 392 Find the amplitude of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = sin x. 5. y = 0.73 sin x The graph of y = 2 sin x may be obtained from the graph of y = sin x by applying a vertical shrink of 0.73.

  3. Homework, Page 392 Find the period of the function and use the language of transformations to describe how the graph of the function is related to the graph of y = cos x. 9. The graph of y = cos (–7 x) may be obtained from the graph of y = cos x by applying a horizontal shrink of 1/7.

  4. Homework, Page 392 Find the amplitude, period, and frequency of the function and use this information to sketch a graph of the function in the window [–3π, 3π] by [–4,4]. 13.

  5. Homework, Page 392 Graph one period of the function. Show the scale on both axes 17.

  6. Homework, Page 392 Graph one period of the function. Show the scale on both axes 21.

  7. Homework, Page 392 Graph three period of the function. Show the scale on both axes. 25.

  8. Homework, Page 392 Specify the period and amplitude of each function. Give the viewing window in which the graph is shown. 29.

  9. Homework, Page 392 Specify the period and amplitude of each function. Give the viewing window in which the graph is shown. 33.

  10. Homework, Page 392 Identify the maximum and minimum values and the zeroes of the function in the interval [–2π, 2π]. 37.

  11. Homework, Page 392 41.

  12. Homework, Page 392 Describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. 45.

  13. Homework, Page 392 Describe the transformations required to obtain the graph of y2 from the graph of y1. 49.

  14. Homework, Page 392 Select the pair of functions that have identical graphs.. 53.

  15. Homework, Page 392 Construct a sinusoid with the given amplitude that goes through the given point. 57.

  16. Homework, Page 392 State the amplitude and period of the sinusoid and (relative to the basic function) the phase shift and vertical translation. 61. The function has an amplitude of 2, a period of 2 π, a phase shift of 3π/4, and a vertical translation of +1.

  17. Homework, Page 392 State the amplitude and period of the sinusoid and (relative to the basic function) the phase shift and vertical translation. 65. The function has an amplitude of 2, a period of 1, no phase shift, and a vertical translation of +1.

  18. Homework, Page 392 Find values of a, b, h, and k so that the graph of the function y = a sin (b(x– h)) + k. 69.

  19. Homework, Page 392 73. A Ferris wheel 50 ft in diameter makes one revolution every 40 sec. If the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground?

  20. Homework, Page 392 77. A block mounted on a spring is set into motion directly above a motion detector, which registers the distance to the block in 0.1 sec intervals. When the block is released, it is 7.2 cm above the detector. The table shows the data collected by the motion detector during the first two sec, with distance d measured in cm. a. Make a scatterplot of d as a function of t and estimate the maximum value of d visually. Use this number and the stated minimum of 7.2 to compute the amplitude.

  21. Homework, Page 392 77. a. Make a scatterplot of d as a function of t and estimate the maximum value of d visually. Use this number and the stated minimum of 7.2 to compute the amplitude. b. Estimate the period of the motion from the scatter plot.

  22. Homework, Page 392 77. c. Model the motion of the block as a sinusoidal function d (t). d. Graph the function with the scatterplot to support the model graphically.

  23. Homework, Page 392 81. The graph of y = sin 2x has half the period of the graph of y = sin 4x. Justify your answer. False, the graph of y = sin 2x has twice the period of the graph of y = sin 4x because

  24. Homework, Page 392 85. The period of the function f (x) = 210 sin (420x +840) is a. b. c. d. e.

  25. Homework, Page 392 89. A piano tuner strikes a tuning fork for the note middle C and creates a sound wave modeled by y = 1.5 sin 524 πt, where t is the time in seconds. (a) What is the period of the function? (b) What is the frequency f = 1/p of this note? (c) Graph the function.

  26. 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant

  27. What you’ll learn about • The Tangent Function • The Cotangent Function • The Secant Function • The Cosecant Function … and why This will give us functions for the remaining trigonometric ratios.

  28. Asymptotes of the Tangent Function

  29. Zeros of the Tangent Function

  30. Asymptotes of the Cotangent Function

  31. Zeros of the Cotangent Function

  32. The Secant Function

  33. The Cosecant Function

  34. Basic Trigonometry Functions

  35. Example Analyzing Trigonometric Functions Analyze the function for domain, range, continuity, increasing or decreasing, symmetry, boundedness, extrema, asymptotes, and end behavior

  36. Example Transformations of Trigonometric Functions Describe the transformations required to obtain the graph of the given function from a basic trigonometric function.

  37. Example Solving Trigonometric Equations Solve the equation for x in the given interval.

  38. Example Solving Trigonometric Equations With a Calculator Solve the equation for x in the given interval.

  39. Example Solving Trigonometric Word Problems A hot air balloon is being blow due east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from point P to the balloon. The angle changes as the balloon travels. a. Express the horizontal distance x as a function of the angle y. b. When the angle is , what is the horizontal distance from P? c. An angle of is equivalent to how many degrees?

  40. Homework • Homework Assignment #30 • Read Section 4.6 • Page 401, Exercises: 1 – 65 (EOO)

  41. 4.6 Graphs of Composite Trigonometric Functions

  42. Quick Review

  43. Quick Review Solutions

  44. What you’ll learn about • Combining Trigonometric and Algebraic Functions • Sums and Differences of Sinusoids • Damped Oscillation … and why Function composition extends our ability to model periodic phenomena like heartbeats and sound waves.

  45. Example Combining the Cosine Function with x2

  46. Example Combining the Cosine Function with x2

  47. Sums That Are Sinusoidal Functions

  48. Sums That Are Not Sinusoidal Functions

  49. Example Identifying a Sinusoid

  50. Example Identifying a Sinusoid

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