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Homework, Page 411

Homework, Page 411. Graph the function from -2 π ≤ x ≤ 2π. State whether or not the function appears to be periodic. 1. f ( x ) is periodic . Homework, Page 411. Graph the function from -2 π ≤ x ≤ 2π. State whether or not the function appears to be periodic. 5. f ( x ) is not periodic .

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Homework, Page 411

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  1. Homework, Page 411 Graph the function from -2π ≤ x ≤ 2π. State whether or not the function appears to be periodic. 1. f (x) is periodic

  2. Homework, Page 411 Graph the function from -2π ≤ x ≤ 2π. State whether or not the function appears to be periodic. 5. f (x) is not periodic

  3. Homework, Page 411 Verify algebraically that the function is periodic and determine its period graphically. Sketch the graph showing two periods. 9.

  4. Homework, Page 411 State the range and domain of the function and sketch a graph showing four periods. 13.

  5. Homework, Page 411 State the range and domain of the function and sketch a graph showing four periods. 17.

  6. Homework, Page 411 The graph of the function oscillates between two parallel lines. Find equations for the lines and graph the lines and the function. 21.

  7. Homework, Page 411 Determine whether f (x) is a sinusoid. 25.

  8. Homework, Page 411 Find a, b, and h so that f (x) ≈ a sin (b(x – h) 29.

  9. Homework, Page 411 Find a, b, and h so that f (x) ≈ a sin (b(x – h) 33.

  10. Homework, Page 411 The function is periodic, but not a sinusoid. Find the period graphically and sketch one period) 37.

  11. Homework, Page 411 Match the function with its graph. 41. c.

  12. Homework, Page 411 Tell whether the function exhibits damped oscillation. If so, identify the damping factor and tell whether the damping occurs as x→ 0 or x → ∞. 45. There is no damping. The damping function has a constant amplitude.

  13. Homework, Page 411 Graph both f and plus or minus its damping factor in the same viewing window. Describe the behavior of f for f > 0. What is the end behavior of f? 49.

  14. Homework, Page 411 Find the period and graph the function over two periods. 53.

  15. Homework, Page 411 Graph f over [-4π, 4π]. Determine whether the function is periodic and, if it is, state the period. 57.

  16. Homework, Page 411 Graph f over [-4π, 4π]. Determine whether the function is periodic and, if it is, state the period. 61.

  17. Homework, Page 411 Find the domain and range of the function. 65.

  18. Homework, Page 411 Find the domain and range of the function. 69.

  19. Homework, Page 411 73. Example 3 shows that the function is periodic. Explain whether you think that is periodic. The function is not periodic because the while x changes at a uniform rate, x3 does not

  20. Homework, Page 411 Match the function with its graph and state the viewing window. 77. d.

  21. Homework, Page 411 81. The function is periodic. Justify your answer. False. The function sin x is an odd function, the stated function is an even function, that is not periodic.

  22. Homework, Page 411 85. The function is a. discontinuous b. bounded c. even d. odd e. periodic

  23. Homework, Page 411 Predict what the graph will look like. Graph the function in one or more viewing windows, determine the main features, draw a summary sketch. Where applicable, name the period, amplitude, domain, range, asymptotes, and zeros. 89.

  24. Homework, Page 411 Predict what the graph will look like. Graph the function in one or more viewing windows, determine the main features, draw a summary sketch. Where applicable, name the period, amplitude, domain, range, asymptotes, and zeros. 93.

  25. 4.7 Inverse Trigonometric Functions

  26. Quick Review

  27. Quick Review Solutions

  28. What you’ll learn about • Inverse Sine Function • Inverse Cosine and Tangent Functions • Composing Trigonometric and Inverse Trigonometric Functions • Applications of Inverse Trigonometric Functions … and why Inverse trig functions can be used to solve trigonometric equations.

  29. Leading Questions The range for the arccosine function is [– 1, 1] The range of the arcsine function is [–π/2,π/2] sec –1 x = cos –1x –1 sin (sin –1 x) = cosx

  30. Inverse Sine Function

  31. Inverse Sine Function (Arcsine Function)

  32. Example Evaluate sin-1x Without a Calculator

  33. Example Evaluate sin-1x Without a Calculator

  34. Inverse Cosine (Arccosine Function)

  35. Inverse Cosine (Arccosine Function)

  36. Inverse Tangent Function (Arctangent Function)

  37. Inverse Tangent Function (Arctangent Function)

  38. End Behavior of the Tangent Function Recognizing that the graphs of inverse functions are reflected about the line y = x, we see that vertical asymptotes of y = tan x become the horizontal asymptotes of y = tan–1x and the range of y = tan x becomes the domain of y = tan–1x .

  39. Composing Trigonometric and Inverse Trigonometric Functions

  40. Example Composing Trig Functions with Arcsine

  41. Example Applying Inverse Trig Functions A person is watching a balloon rise straight up from a place 500 ft from the launch point. a. Write θ as a function of s, the height of the balloon. b. Is the change in θ greater as s changes from 10 ft to 20 ft or as s changes from 200 ft to 210 ft? Explain.

  42. Example Applying Inverse Trig Functions c. In the graph of this relationship, does the x-axis represent s height and the y-axis represent θ (in degrees) or vice-versa? Explain.

  43. Following Questions The angle of depression tells us how depressing an equation is relative to an equation of known depression. The angle of elevation is measured from the horizontal upwards. Simple harmonic motion is repetitive motion such as that of a pendulum. The frequency of an object in simple harmonic motion refers to the number of times it passes through a given point per unit time.

  44. Homework • Homework Assignment #32 • Review Section 4.7 • Page 421, Exercises: 1 – 69 (EOO) • Quiz next time

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