66. Tides One day the tide at a point in Maine could be modeled by h = 5 cos 2 π 13 t , h equals 5 cosine . fraction 2 pi , over 13 end fraction , t . comma where h is the height of the tide in feet above the mean water level and t is the number of hours past midnight. At what times that day would the tide have been each of the following?
    1. 3 ft above the mean water level
    2. at least 3 ft above the mean water level

Standardized Test Prep

SAT/ACT

67. Which of the following is NOT equal to 60 ° ? 60 degrees question mark
    1. sin − 1 3 2 sine super negative 1 end super . fraction square root of 3 , over 2 end fraction
    2. cos − 1 1 2 cosine super negative 1 end super . 1 half
    3. tan − 1 3 tangent super negative 1 end super . square root of 3
    4. tan − 1 3 3 tangent super negative 1 end super . fraction square root of 3 , over 3 end fraction
68. In which quadrants are the solutions to tan θ + 1 = 0 ? tangent theta plus 1 equals 0 question mark
    6. Quadrants I and II
    7. Quadrants II and III
    8. Quadrants II and IV
    9. Quadrants III and IV
69. Which of these angles have a sine of about − 0.6 ? negative 0.6 question mark
    1. 143 . 1 ° 143 . 1 degrees
    2. 216 . 9 ° 216 . 9 degrees
    3. 323 . 1 ° 323 . 1 degrees
    1. I and II only
    2. I and III only
    3. I, II, and III
    4. II and III only
70. What are the solutions of 2 sin θ − 3 = 0 2 sine theta negative square root of 3 equals 0 for 0 ≤ θ < 0 less than or equal to , theta less than 2π?
    6. π 6 pi over 6 and 5 π 6 fraction 5 pi , over 6 end fraction
    7. π 3 pi over 3 and 2 π 3 fraction 2 pi , over 3 end fraction
    8. 2 π 3 fraction 2 pi , over 3 end fraction and 4 π 3 fraction 4 pi , over 3 end fraction
    9. 4 π 3 fraction 4 pi , over 3 end fraction and 5 π 3 fraction 5 pi , over 3 end fraction
71. Suppose a > 0 . eh greater than 0 . Under what conditions for a and b will a sin θ = b eh sine theta equals b have exactly two solutions in the interval 0 ≤ θ < 2 π ? 0 less than or equal to . theta less than 2 pi question mark
    1. a = b eh equals b
    2. b > a b greater than , eh
    3. a = − b eh equals negative b
    4. a > b > − a eh greater than , b greater than negative eh

Extended Response

72. Solve 2 sin 2 θ = − sin θ 2 , sine squared , theta equals negative sine theta for θ theta with 0 ≤ θ < 2 π . 0 less than or equal to theta less than 2 pi . Show your work.

Mixed Review

Simplify each expression. See Lesson 14-1.

73. cos 2 θ sec θ csc θ cosine squared , theta secant theta co-secant theta
74. sin θ sec θ tan θ sine theta secant theta tangent theta
75. csc 2 θ ( 1 − cos 2 θ ) co-secant squared , theta open 1 minus , cosine squared , theta close
76. cos θ csc θ cot θ fraction cosine theta co-secant theta , over co-tangent theta end fraction
77. sec θ cot θ + tan θ fraction secant theta , over co-tangent theta plus tangent theta end fraction
78. sin θ + tan θ 1 + cos θ fraction sine theta plus tangent theta , over 1 plus cosine theta end fraction

Write a cosine function for each description. See Lesson 13-5.

79. amplitude 4, period 8
80. amplitude 3, period 2π
81. amplitude π 4 , pi over 4 , comma period 3 π 3 pi

Get Ready! To prepare for Lesson 14-3, do Exercises 82–84.

Solve each proportion. See p. 966.

82. x 7 = 28 49 x over 7 , equals , 28 over 49
83. 10 14 = 15 x 10 over 14 , equals , 15 over x
84. 21 10 = x 25 21 over 10 , equals , x over 25

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