Standardized Test Prep

SAT/ACT

46. Which function has a period of 2π and an amplitude of 4?
    1. f ( x ) = 2 cos 4 θ f open x close equals 2 cosine 4 theta
    2. f ( x ) = 4 cos 2 θ f open x close equals 4 cosine 2 theta
    3. f ( x ) = 2 cos θ f open x close equals 2 cosine theta
    4. f ( x ) = 4 cos θ f open x close equals 4 cosine theta

47. Which equation corresponds to the graph shown below? The screen dimensions are − 4 π ≤ x ≤ 4 π  and  − 2 ≤ y ≤ 2 . negative 4 pi less than or equal to x less than or equal to 4 pi , and , minus 2 less than or equal to y less than or equal to 2 .

    

    6. y = 1 2 cos x 4 y equals , 1 half cosine , x over 4
    7. y = 2 cos x 4 y equals 2 cosine , x over 4
    8. y = 1 2 cos 4 x y equals , 1 half cosine 4 x
    9. y = 2 cos 4 x y equals 2 cosine 4 x
48. Which equation has the same graph as y = − cos t ? y equals negative cosine t question mark
    1. y = cos ( − t ) y equals cosine open negative t close
    2. y = sin ( t − π ) y equals sine open t minus pi close
    3. y = cos ( t − π ) y equals cosine open t minus pi close
    4. y = − sin t y equals negative sine t
49. How many solutions does the equation 1 = − sin 2 t 1 equals negative sine 2 t  have for 0 ≤ t ≤ 2 π ? 0 less than or equal to t less than or equal to 2 pi question mark
    6. 1
    7. 2
    8. 3
    9. 4

Short Response

50. What are the amplitude and period of y = − 0.2 cos π 3 θ ? y equals negative 0.2 cosine , fraction pi , over 3 end fraction , theta question mark

Mixed Review

Sketch one cycle of each sine curve. Assume that a > 0 . eh greater than 0 .  Then write an equation for each graph. See Lesson 13-4.

51. amplitude 1, period π 3 pi over 3
52. amplitude 2.5, period π
53. amplitude 4, period 1

Find the sample size that produces each margin of error. See Lesson 11-7.

54. ± 3 % plus minus 3 percent
55. ± 7 % plus minus 7 percent
56. ± 11 % plus minus 11 percent

Write the explicit formula for each geometric sequence. Then, list the first five terms. See Lesson 9-3.

57. a 1 = 10 ,  r = 3 eh sub 1 , equals 10 comma r equals 3
58. a 1 = 12 , r = − 0.3 eh sub 1 , equals 12 comma r equals negative 0.3
59. a 1 = 900 ,  r = − 1 3 eh sub 1 , equals 900 , comma r equals negative , 1 third

Get Ready! To prepare for Lesson 13-6, do Exercises 60–65.

Graphing Calculator Use a calculator to find the sine and cosine of each value of θ. Then calculate the ratio sin θ cos θ . fraction sine theta , over cosine theta end fraction . .  Round answers to the nearest thousandth, if necessary. See Lesson 13-5.

60. π 3  radians pi over 3 . radians
61. 30 degrees
62. 90 degrees
63. 5 π 6  radians fraction 5 pi , over 6 end fraction . radians
64. 5 π 2  radians fraction 5 pi , over 2 end fraction . radians
65. 0 degrees

Table of Contents