Answers to Trigonometry Practice Exam
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(1)
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FALSE
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(2)
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TRUE
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(3)
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FALSE (In general, unless A = 45°)
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(4)
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FALSE
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(5)
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TRUE
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(6)
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FALSE
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(7)
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FALSE
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(8)
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TRUE
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(9)
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FALSE
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(10)
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TRUE
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(11)
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The exact length is Ö13.
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(12)
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The exact length is 3Ö5.
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(13)
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Angle B = 50° and Angle A = 40°. Side h = Ö61, while Side x = 12. Side H = 2Ö61.
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(14)
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The sum is 69° 6¢5¢¢.
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(15)
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The decimal measure is 35.5042°.
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(16)
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The degree-minute-second measure is 25° 33¢11¢¢.
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(17)
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The exact values are sinA = 3/Ö10 and cosA = -1/Ö10.
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(18)
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The reference angle for A = -210° will be 30°. The reference angle for
B will be 79° 45¢.
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(19)
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Since A = -210° lies in Quadrant II and has reference angle 30°, we know
that sec(-210°) = -2/Ö3.
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(20)
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Let A be the angle of elevation. Since the woman is five feet tall, we know that
tanA = 5/12. Let y be the height of the lamp. We then know that tanA = y/22. Hence, we
know that y/22 = 5/12, which implies that y = 55/6 feet.
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(21)
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The radian measure is 3p.
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(22)
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The degree measure is 310°.
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(23)
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The reference angle for 25 p/3 is p/3. The angle 25 p/3 lies in Quadrant
I; hence, sin(25 p/3) = sin(p/3) = Ö3 / 2.
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(24)
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In one week the moon will travel about one quarter of the way around its orbit.
Hence, the moon will travel through an angle of p/2 radians in one week. The total distance
the moon travels will therefore be L = 242,950(p/2) » 381,624 miles.
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(25)
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FALSE
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(26)
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FALSE
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(27)
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TRUE
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(28)
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TRUE
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(29)
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FALSE
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(30)
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TRUE
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(31)
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Let A denote the first boat and let B denote the boat that is fifteen miles due
east of the first. The distance from A to the lighthouse will be b » 11 miles and the
distance from B to the lighthouse will be a » 13 miles.
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(32)
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Using the Law of cosines, the magnitude of v+w is approximately 32.
The bearing will be approximately 83°.
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(33)
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No, the defendant is lying. According to his statement, the Law of Sines tells us
that sinA = 3/2, which is impossible.
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(34)
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In this interval, sinx = 0 when x = -p, 0, and p.
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(35)
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In this interval secx is undefined when x = p/2 and x = 3p/2.
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(36)
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The period of the function is p.
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(37)
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The frequency of the function is 2.
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(38)
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The formulas will be y = 1/2 + (3/2) sin[(2/3)(x+p/2)] and y = 1/2 +(3/2) cos[(2/3)(x-p/4)].
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(39)
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The exact value is -p/6.
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(40)
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Let A = Arcsin(6/7). Since we know sin(A) = 6/7, we know the side adjacent to
A must be Ö13. Hence, we know tanA = 6/Ö13.
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(41)
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We know that cos(255°) = cos(300°)cos(45°) +sin(300°)sin(45°). Now, cos(300°) = cos(60°) = 1/2 and sin(300°) = -sin(60°) = -Ö3 / 2. Hence, the exact value is Ö2 / 4 - Ö6 / 4.
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(42)
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We know cos(2A) = 1-2sin2(A) = -1/8.
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(43)
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We know that cos(2A) = 1-2sin2(A), which implies that 5/8 = sin2(A). Since
A lies in Quadrant III, we know sin(A) = -Ö(5/8).
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(44)
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We know the measure of two angles and the side between them; hence, we can use the Law of Sines to find the
length of the side opposite the 40° angle. The pole is about 74.2 feet
tall.
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On 3 Dec 2003, 12:54.