63. Physics When a ray of light passes from one medium into a second, the angle of incidence θ 1 theta sub 1 and the angle of refraction θ 2 theta sub 2 are related by Snell's law: n 1 sin θ 1 = n 2 sin θ 2 , n sub 1 sine , theta sub 1 , equals , n sub 2 sine , theta sub 2 , comma where n 1 n sub 1 is the index of refraction of the first medium and n 2 n sub 2 is the index of refraction of the second medium. How are θ 1 theta sub 1 and θ 2 theta sub 2 related if n 2 > n 1 ? n sub 2 , greater than , n sub 1 , question mark If n 2 < n 1 ? n sub 2 , less than , n sub 1 , question mark If n 2 = n 1 ? n sub 2 , equals , n sub 1 , question mark

    

Standardized Test Prep

SAT/ACT

64. Which expression is equivalent to 2 cot θ ? co-tangent theta question mark
    1. 1 2 tan θ fraction 1 , over 2 tangent theta end fraction
    2. 2 cot θ fraction 2 , over co-tangent theta end fraction
    3. 2 cos θ sin θ fraction 2 cosine theta , over sine theta end fraction
    4. sin θ 1 2 cos θ fraction sine theta , over 1 half cosine theta end fraction
65. Which equation is NOT an identity?
    6. cos 2 θ = 1 − sin 2 θ cosine squared , theta equals 1 minus , sine squared , theta
    7. cot 2 θ = csc 2 θ − 1 co-tangent squared , theta equals , co-secant squared , theta negative 1
    8. sin 2 θ = cos 2 θ − 1 sine squared , theta equals , cosine squared , theta negative 1
    9. tan 2 θ = sec 2 θ − 1 tangent squared , theta equals , secant squared , theta negative 1
66. Which expressions are equivalent?
    1. ( sin θ ) ( csc θ − sin θ ) open sine theta close open co-secant theta negative sine theta close
    2. sin 2 θ − 1 sine squared , theta negative 1
    3. cos 2 θ cosine squared , theta
    1. I and II only
    2. II and III only
    3. I and III only
    4. I, II, and III
67. How can you express csc 2 θ − 2 cot 2 θ  in terms of  sin θ  and  cos θ ? co-secant squared , theta negative 2 , co-tangent squared , theta . intermsof sine theta , and cosine theta question mark
    6. 1 − 2 cos 2 θ sin 2 θ fraction 1 minus 2 , cosine squared , theta , over sine squared , theta end fraction
    7. 1 − 2 sin 2 θ sin 2 θ fraction 1 minus 2 , sine squared , theta , over sine squared , theta end fraction
    8. sin 2 θ − 2 cos 2 θ sine squared , theta negative 2 , cosine squared , theta
    9. 1 sin 2 θ − 1 tan 2 θ fraction 1 , over sine squared , theta end fraction . minus . fraction 1 , over tangent squared , theta end fraction
68. Which expression is equivalent to tan θ cos θ − sec θ ? fraction tangent theta , over cosine theta minus secant theta end fraction . question mark
    1. csc θ co-secant theta
    2. sec θ secant theta
    3. − csc θ negative co-secant theta
    4. tan 2 θ tangent squared , theta

Short Response

69. Show that ( sec θ + 1 )   ( sec θ − 1 ) = tan 2 θ open secant theta plus 1 close open secant theta negative 1 close equals , tangent squared , theta is an identity.

Mixed Review

Graph each function in the interval from 0 to 2π. See Lesson 13-8.

70. y = csc ( − θ ) y equals co-secant open negative theta close
71. y = − sec 0.5 θ y equals negative secant , 0.5 theta
72. y = − sec ( 0.5 θ + 2 ) y equals negative secant open 0.5 theta plus 2 close
73. y = π sec θ y equals pi secant theta

Find the measure of an angle between 0 ° and 360 ° 0 degrees . ehnd , 360 degrees that is coterminal with the given angle. See Lesson 13-2.

74. 395 ° 395 degrees
75. 405 ° 405 degrees
76. − 225 ° negative 225 degrees
77. − 149 ° negative 149 degrees

Get Ready! To prepare for Lesson 14-2, do Exercises 78–80.

For each function f, find f − 1 . f super negative 1 end super , . See Lesson 6-7.

78. f ( x ) = x + 1 f open x close equals x plus 1
79. f ( x ) = 2 x − 3 f open x close equals 2 x minus 3
80. f ( x ) = x 2 + 4 f open x close equals , x squared , plus 4

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