1 / 52

Homework, Page 381

Homework, Page 381. Identify the one angle that is not coterminal with the others. 1. . Homework, Page 381. Evaluate the six trigonometric functions of the angle θ . 5. . Homework, Page 381.

vanna
Télécharger la présentation

Homework, Page 381

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Homework, Page 381 Identify the one angle that is not coterminal with the others. 1.

  2. Homework, Page 381 Evaluate the six trigonometric functions of the angle θ. 5.

  3. Homework, Page 381 Point P is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ. If the function is undefined, write undefined. 9.

  4. Homework, Page 381 State the sign (+ or –) of (a) sin t, (b) cos t (c) tan t for values of t in the interval given. 13.

  5. Homework, Page 381 Determine the sign (+ or –) of the given value without a calculator. 17.

  6. Homework, Page 381 Choose the point on the terminal side of θ. 21. (a) (2, 2) (b) (c) Choice (a) as tan 45º = 1.

  7. Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 25.

  8. Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 29.

  9. Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 33.

  10. Homework, Page 381 Find (a) sin θ, (b) cos θ, and (c) tan θ for the given quadrantal angle. If the value is undefined, write undefined. 37.

  11. Homework, Page 381 Find (a) sin θ, (b) cos θ, and (c) tan θ for the given quadrantal angle. If the value is undefined, write undefined. 41.

  12. Homework, Page 381 Evaluate without using a calculator. 45.

  13. Homework, Page 381 Evaluate by using the period of the function. 49.

  14. Homework, Page 381 53. Use your calculator to evaluate the expressions in Exercises 49 – 52. Does your calculator give the correct answer. Many miss all four. Give a brief explanation why. The calculator algorithms apparently do recognize large multiples of pi and end up evaluating at nearby values.

  15. Homework, Page 381 57. A weight suspended from a spring is set into motion. Its displacement d from equilibrium is modeled by the equation where d is the displacement in inches and t is the time in seconds. Find the displacement at the given time. (a) t = 0 (b) t = 3

  16. Homework, Page 381 61. If θ is an angle in a triangle such that cos θ < 0, then θ is an obtuse angle. Justify your answer. True. An obtuse angle in the standard position would have its terminal side in the second quadrant and cosine is negative in the second quadrant.

  17. Homework, Page 381 65. The range of the function a. [1] b. [-1, 1] c. [0, 1] d. [0, 2] e. [0, ∞]

  18. Homework, Page 381 Find the value of the unique real number θbetween 0 and 2π that satisfies the two given conditions. 69. If tan and sin are negative, cos must be positive. The angle must be in the fourth quadrant and the reference angle is π/4, so θ = 2π – π/4 = 7π/4

  19. 4.4 Graphs of Sine and Cosine: Sinusoids

  20. What you’ll learn about • The Basic Waves • Sinusoids and Transformations • Modeling Periodic Behavior with Sinusoids … and why Sine and cosine gain added significance when used to model waves and periodic behavior.

  21. Leading Questions A function is a sinusoid if it can be written in the form y = a sin (bx + c) +d, where a and b ≠ 0. The function y = a cos (bx + c) +d is not a sinusoid. The amplitude of a sinusoid is |a|. The period of a sinusoid is |b|/2π. The frequency of a sinusoid is |b|/2π. Sinusoids are often used to model the behavior of periodic occurrences.

  22. Sinusoid

  23. Amplitude of a Sinusoid

  24. Example Finding Amplitude Find the amplitude of each function and use the language of transformations to describe how the graphs are related. (a) (b) (c)

  25. Period of a Sinusoid

  26. Example Finding Period and Frequency Find the period and frequency of each function and use the language of transformations to describe how the graphs are related. (a) (b) (c)

  27. Example Horizontal Stretch or Shrink and Period

  28. Frequency of a Sinusoid

  29. Example Combining a Phase Shift with a Period Change

  30. Graphs of Sinusoids

  31. Constructing a Sinusoidal Model using Time

  32. Constructing a Sinusoidal Model using Time

  33. Example Constructing a Sinusoidal Model

  34. Example Constructing a Sinusoidal Model

  35. Following Questions The period of the tangent function is 2π. Tangent is an odd function. Cotangent is an even function. The graph of cosecant has relative minimum values, but no absolute minimum value. Some trig equations may be solved algebraically. Most trig equations may be solved graphically.

  36. Homework • Homework Assignment #29 • Read Section 4.5 • Page 392, Exercises: 1 – 89 (EOO)

  37. 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant

  38. Quick Review

  39. Quick Review Solutions

  40. 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.

  41. Asymptotes of the Tangent Function

  42. Zeros of the Tangent Function

  43. Asymptotes of the Cotangent Function

  44. Zeros of the Cotangent Function

  45. The Secant Function

  46. The Cosecant Function

  47. Basic Trigonometry Functions

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

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

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

More Related