Download Trig Final Exam Review

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
′
′′
1) 56°35 43
A) 56.56°
B) 56.61°
C) 56.60°
D) 56.66°
Convert the angle to degrees, minutes, and seconds.
2) 40.78°
′
′′
′
′′
A) 40°46 54
B) 40°46 78
′
′′
C) 40°46 36
Find the angle of least positive measure coterminal with the given angle.
3) 500°
A) 250°
B) 130°
C) 140°
′
B) 120°
C) 60°
1
′′
2)
D) 40°46 48
3)
D) 320°
Solve the problem.
4) Find the measure of the smaller angle formed by the hands of the clock shown.
A) 110°
1)
D) 150°
4)
Sketch an angle θ in standard position such that θ has the least positive measure and the given point is on the terminal
side of θ.
5) (-2, 5)
5)
y
x
A)
B)
C)
D)
Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the
given value is a decimal, round your answer to three decimal places.
6) tan θ, given that cot θ = - 6
6)
7
A)
13
7
B)
7
6
C) - 7
6
Identify the quadrant for the angle θ satisfying the following conditions.
7) cot θ < 0 and cos θ > 0
A) Quadrant II
B) Quadrant IV
C) Quadrant I
2
D) - 6
7
7)
D) Quadrant III
Evaluate the function requested. Write your answer as a fraction in lowest terms.
8)
8)
30
18
24
Find sin A.
A) sin A = 4
3
B) sin A = 4
5
C) sin A = 5
4
D) sin A = 3
5
Without using a calculator, give the exact trigonometric function value with rational denominator.
9) cos 60°
A)
1
2
B)
2
C)
2
3
D)
3
2
Solve the problem for the given information.
10) Find the equation of a line passing through the origin so that the cosine of the angle between the
line in quadrant I and the positive x-axis is 1 .
2
A) y =
3
3x
B) y =
2
3x
C) y =
3x
9)
10)
D) y = 1 x
2
Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
11) tan θ = 1.9527292
11)
A) 117.117157°
B) 242.882843°
C) 27.1171573°
D) 62.8828427°
Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
′
12) tan 63°18
12)
A) 1.9885787
B) 1.9882787
C) 1.9888787
D) 1.9891787
3
Solve the right triangle. If two sides are given, give angles in degrees and minutes.
13)
B = 68°14', b = 17 km
Round side lengths to one decimal place.
A) A = 21°46'; c = 18.3 km; a = 45.7 km
C) A = 21°46'; c = 45.8 km; a = 6.8 km
13)
B) A = 21°46'; c = 45.8 km; a = 18.3 km
D) A = 21°46'; c = 18.3 km; a = 6.8 km
Find the corresponding angle measure in radians.
14) 120°
14)
1
-1
1
r
-1
A) π
6
B) 3π
2
C) 7π
6
D) 2π
3
Find the length of an arc intercepted by a central angle θ in a circle of radius r. Round your answer to 1 decimal place.
15) r = 26.13 cm.; θ = 7 π radians
15)
6
A) 47.9 cm
B) 191.5 cm
C) 30.5 cm
D) 95.8 cm
Find the exact value without using a calculator.
16) cos 2π
3
A)
3
2
16)
C) - 1
2
B) undefined
D) -
3
2
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
5π
17)
12
A) 144°
B) 75°
C) 150°
4
17)
D) 432π°
Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
18) Find the distance between City A, 62° N and City B, 29° N. (Round to the nearest kilometer.)
A) 3624 km
B) 3715 km
C) 3686 km
D) 3777 km
18)
Solve the problem.
19) Through how many radians will the hour hand on a clock rotate in 48 hours?
A) 8π
B) 16π
C) π
D) 12π
19)
Convert the degree measure to radians. Leave answer as a multiple of π.
20) 530°
A) 17π
B) 53π
C) 53π
18
18
36
20)
D) 53π
9
Solve the problem.
′
21) The angle of elevation from a point on the ground to the top of a tower is 35° 16 . The angle of
′
elevation from a point 130 feet farther back from the tower is 24° 18 . Find the height of the
tower. Round to the nearest foot.
A) 162 ft
B) 1624 ft
C) 158 ft
D) 173 ft
22) On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is
40 meters long and the tree is 32 meters tall, how long is the shadow?
A) 51 m
B) 72 m
C) 64 m
D) 24 m
21)
22)
Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
23) cos θ = -
3
23)
2
A) 60° and 120°
B) 150° and 210°
C) 210° and 330°
Solve the right triangle.
24) B = 34.4°, c = 4.6 mm, C = 90°
Round values to one decimal place.
A) a = 3 mm, A = 55.6°, b = 3.5 mm
C) a = 2.6 mm, A = 55.6°, b = 3.8 mm
D) 60° and 300°
24)
B) a = 3.8 mm, A = 55.6°, b = 2.6 mm
D) a = 3.8 mm, A = 55.6°, b = 3 mm
Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest
tenth.
25) r = 18.0 ft, θ = 2π radians
25)
3
A) 678.6 ft2
B) 339.3 ft2
C) 39.5 ft2
D) 18.8 ft2
Solve the problem.
26) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin
θ, where W is the weight of the car and θ is the angle of the hill's grade (θ > 0 for uphill travel, θ <
0 for downhill travel). What is the grade resistance (to the nearest pound) of a 2000-lb car
traveling uphill on a 2° grade (θ = 2°)?
A) 2002 lb
B) -70 lb
C) 70 lb
D) -2002 lb
5
26)
Find the exact circular function value.
27) sin 3π
4
A) - 1
2
27)
B)
1
2
C) -
2
D)
2
2
2
Graph the function.
28) y = 3 cos 3 x
2
4
28)
y
2
1
-4π
3
4π
3
x
-1
-2
A)
B)
y
y
2
2
1
1
-4π
3
4π x
3
-4π
3
4π x
3
-1
-1
-2
-2
C)
D)
y
y
2
2
1
1
-4π
3
4π
3
-4π
3
x
4π x
3
-1
-1
-2
-2
6
Use Identities to find the exact value.
29) cos 255°
24
A)
6
29)
B)
2-
6
C)
6-
2
64
D)
2
Use a sum or difference identity to find the exact value.
30) sin 15°
6+
4
A)
2
64
B)
30)
2
C)
-
6+
4
2
D)
-
64
2
Solve the problem.
31) The voltage E in an electrical circuit is given by E = 4.1 cos 140πt, where t is time measured in
seconds. Find the period.
π
1
A) 70
B) 70π
C)
D)
70
70
31)
The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
32) Find cos θ.
32)
- 5 , 12
13 13
A) - 12
13
B)
12
13
C) - 5
13
D) - 5
12
Find the exact value of the real number y.
33) y = cos-1
A)
π
4
2
33)
2
B)
11π
6
C)
7
π
6
D)
7π
4
Use an identity to write the expression as a single trigonometric function or as a single number.
34)
1 + cos 24°
2
A) tan 12°
34)
B) sin 12°
Find the exact value by using a half-angle identity.
35) sin 75°
1
2- 3
A) - 1
2- 3
B)
2
2
C) cot 12°
D) cos 12°
1
C)
2
D) - 1
2
35)
2+
3
2+
3
Use identities to find the indicated value for each angle measure.
36) sin θ = - 4 , 3π < θ < 2π
Find cos(2θ).
5
2
A) - 7
25
B)
7
25
Use a sum or difference identity to find the exact value.
37) tan 75°
A) - 3 - 2
B) 3 - 2
36)
C) - 24
25
D)
C) -
D)
24
25
37)
3 +2
3 +2
Solve the problem.
38) Find ω for a spoke on a bike tire revolving 85 times per minute.
π radians per min
A)
B) 85π radians per min
170
C) 170π radians per min
D)
38)
π radians per min
85
Find the exact values of s in the given interval that satisfy the given condition.
39) [0, 2π); cos s = 1
2
A) π , 5π
3 3
B) π , 7π
4 4
C) π , 3π
2 2
39)
D) π , 11π
6 6
Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
40) cos s = 0.6577
A) 0.7178
B) 5.4302
C) 0.8530
D) 0.9946
40)
Solve the problem.
41) Find the radius of a circle in which a central angle of π radian determines a sector of area
7
72 square meters. Round to the nearest hundredth.
A) 17.91 m
B) 25.33 m
8
C) 320.86 m
D) 12.67 m
41)
42) A pendulum swinging through a central angle of 133° completes an arc of length 11.3 cm. What
is the length of the pendulum? Round to the nearest hundredth.
A) 4.77 cm
B) 4.97 cm
C) 4.67 cm
D) 4.87 cm
Find the exact value of the expression.
43) sec 45°
A)
2
B)
42)
43)
C) 2
3
Find the reference angle for the given angle.
44) -26.1°
A) 26.1°
B) 64.4°
3
3
2
D)
2
44)
C) 26.6°
D) 63.9°
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
45) Find sin A when a = 7 and b = 6.
45)
A)
6
85
85
B)
85
6
C)
85
7
D)
7
85
85
Use the fundamental identities to find the value of the trigonometric function.
46) Find tan θ, given that sin θ = 3 and θ is in quadrant II.
4
A)
5
4
B) - 3
7
C) - 3
2
7
46)
D) -
7
9
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
47) csc (608°) and cot (608°)
47)
A) negative and negative
B) negative and positive
C) positive and positive
D) positive and negative
If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
48) IV, x
48)
y
A) Positive
B) Negative
Evaluate the expression.
49) cos 450°
A) 1
49)
B) Undefined
C)
9
3
2
D) 0
Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the
indicated trig function for θ.
50) (6, 8); Find cos θ.
50)
4
3
3
4
A)
B)
C)
D)
3
5
4
5
10
Answer Key
Testname: FINAL REVIEWNET
1) C
2) D
3) C
4) B
5) B
6) C
7) B
8) B
9) A
10) C
11) D
12) B
13) D
14) D
15) D
16) C
17) B
18) C
19) A
20) B
21) A
22) D
23) B
24) B
25) B
26) C
27) D
28) C
29) A
30) B
31) D
32) C
33) A
34) D
35) C
36) A
37) D
38) C
39) A
40) C
41) A
42) D
43) A
44) A
45) D
46) B
47) B
48) B
49) D
11
Answer Key
Testname: FINAL REVIEWNET
50) B
12