# Answers to Trigonometry Practice Exam

(1)
FALSE
(2)
TRUE
(3)
FALSE (In general, unless A = 45°)
(4)
FALSE
(5)
TRUE
(6)
FALSE
(7)
FALSE
(8)
TRUE
(9)
FALSE
(10)
TRUE
(11)
The exact length is Ö13.
(12)
The exact length is 3Ö5.
(13)
Angle B = 50° and Angle A = 40°. Side h = Ö61, while Side x = 12. Side H = 2Ö61.
(14)
The sum is 69° 6¢5¢¢.
(15)
The decimal measure is 35.5042°.
(16)
The degree-minute-second measure is 25° 33¢11¢¢.
(17)
The exact values are sinA = 3/Ö10 and cosA = -1/Ö10.
(18)
The reference angle for A = -210° will be 30°. The reference angle for B will be 79° 45¢.
(19)
Since A = -210° lies in Quadrant II and has reference angle 30°, we know that sec(-210°) = -2/Ö3.
(20)
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.
(21)
(22)
The degree measure is 310°.
(23)
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.
(24)
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.
(25)
FALSE
(26)
FALSE
(27)
TRUE
(28)
TRUE
(29)
FALSE
(30)
TRUE
(31)
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.
(32)
Using the Law of cosines, the magnitude of v+w is approximately 32. The bearing will be approximately 83°.
(33)
No, the defendant is lying. According to his statement, the Law of Sines tells us that sinA = 3/2, which is impossible.
(34)
In this interval, sinx = 0 when x = -p, 0, and p.
(35)
In this interval secx is undefined when x = p/2 and x = 3p/2.
(36)
The period of the function is p.
(37)
The frequency of the function is 2.
(38)
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)].
(39)
The exact value is -p/6.
(40)
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.
(41)
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.
(42)
We know cos(2A) = 1-2sin2(A) = -1/8.
(43)
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).

(44)
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.

File translated from TEX by TTH, version 2.80.
On 3 Dec 2003, 12:54.