Chapter 10 - NCPN

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Practice and Problem Solving Identify the amplitude, period, and number of cycles in the interval from 0 to 2π for each trigonometric function. (Assume that θ is given in radians.) 6. y = 1.5sin 2θ 7. y = 4cos θ 8. y = –2sin θ 9. y = 3cos θ 2 10. y = 0.2cos 0.2θ 11. y = –1.5sin θ 3 12. y = 3sin (θ + π) 13. y = cos ( θ − π ) 1 2 2 2 Identify the period and the location of two vertical asymptotes for each function. (Assume that θ is given in radians.) 14. y = tan 2θ 15. y = 3tan θ 1 2 1 3 16. y = 7.5tan θ 2 17. y = 2tan (θ + π) Graph each trigonometric function over the specified domain. 18. y = 2cos 2θ, 0 ≤ θ ≤ 2π 19. y = sin 2θ, 0 ≤ θ ≤ 360° 20. y = tan 2θ, –180° ≤ θ ≤ 180° 21. y = 2cos θ, –2π ≤ θ ≤ 2π 22. y = tan ≠ θ, –4.5 ≤ θ ≤ 4.5 23. y = –1.5sin θ, –2π ≤ θ ≤ 2π 3 24. Sounds traveling through the air can be modeled by sine waves. The sound of a car horn can be represented by the function y = 8sin 160θ. a. The loudness of a sound is related to the amplitude of its sound wave. Write a new function for a sound that is twice as loud as the car horn. b. Sounds are caused by vibrations. When an object vibrates twice as fast, it produces a sound with a pitch that is one octave higher. The period of the sound wave is half the original period. Write a new function for a sound that is the same loudness as the car horn, but one octave higher. c. Graph the function modeling the sound of the car horn over the interval 0 ≤ θ ≤ 0.1. 460 Chapter 10 Trigonometric Functions and Identities
25. The function y = 3sin ≠ t models the position of a fishing boat on 4 the ocean relative to sea level. The independent variable t is given in seconds, and the dependent variable y is given in feet above or below sea level. a. Graph the trigonometric function for values of θ between 0 and 12 seconds. b. How long does it take the boat to complete one full cycle as it rides the waves of the ocean c. What is the amplitude of the function What is the physical interpretation of this value d. How would the equation of the function change if the boat were riding on a 4-foot wave y = 4 sin π t Mixed Review Determine if each sequence is arithmetic. If so, state the common difference of the sequence. 26. 4, 12, 20, 28, 36, … 27. 1, 2, 4, 7, 11, … Find the area of each triangle. Round your answers to the nearest tenth if necessary. 28. 4 29. 30. A cereal box has a width of 2x inches, a length of 4x + 1 inches, and a height of 6x + 1 inches. Write an expression for the volume of the box. Then find the volume of the cereal box if x = 1.5 inches. 10.4 Graphing Trigonometric Functions 461
Page 1 and 2: Chapter 10 Contents 10.1 Right Tria
Page 3 and 4: Lesson 10.1 Right Triangle Trigonom
Page 5 and 6: Solution Use the definitions of the
Page 7 and 8: Solve for x in each right triangle.
Page 9 and 10: 30. A wheelchair ramp is 20 feet lo
Page 11 and 12: Arc Length The unit circle has a ra
Page 13 and 14: Using a Calculator A scientific cal
Page 15 and 16: Find the length of the intercepted
Page 17 and 18: Lesson 10.3 Inverse Trigonometric F
Page 19 and 20: see margin After taking off, a comm
Page 21 and 22: 20. What is the angle of descent of
Page 23 and 24: The y-values on the unit circle are
Page 25 and 26: Example 2 Graphing Cosine Functions
Page 27: Activity Using a Graphing Calculato
Page 31 and 32: Ongoing Assessment In PQR, m∠P =
Page 33 and 34: Activity Ambiguous Cases Two triang
Page 35 and 36: Lesson Assessment Think and Discuss
Page 37 and 38: 23. Two points in a forest, A and B
Page 39 and 40: Lesson 10.6 Verifying Trigonometric
Page 41 and 42: Activity 2 Using the Pythagorean Id
Page 43 and 44: Lesson 10.7 Angle Sum and Differenc
Page 45 and 46: Practice and Problem Solving Use a
Page 47 and 48: Lesson 13.4 Double-Angle and Half-A
Page 49 and 50: When Trigonometric Function Values
Page 51 and 52: Practice and Problem Solving Use a
Page 53 and 54: Lesson 10.9 Solving Trigonometric E
Page 55 and 56: Use the Zero-Product Property to se
Page 57 and 58: Practice and Problem Solving Solve
Page 59 and 60: Math Labs Activity 1: The Circle of
Page 61 and 62: Activity 3: The Sine Curve of Biorh
Page 63 and 64: 3 Hold a protractor upside down so
Page 65 and 66: 3 Cale, Tammie, and Allison are mem
Page 67 and 68: 8 Bella does freelance marketing wo
Page 69 and 70: Health Occupations 13 Dmitri wants
Page 71 and 72: Lessons 10.5 and 10.6 Review Exampl
Page 73: Standardized Test Practice Multiple

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