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 degreeminutesecond 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)

The radian measure is 3p.

(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)(xp/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) = 12sin^{2}(A) = 1/8.

(43)

We know that cos(2A) = 12sin^{2}(A), which implies that 5/8 = sin^{2}(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.
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On 3 Dec 2003, 12:54.