Download Exam Name___________________________________

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a calculator to give the value to the nearest degree.
1) = sin-1 (-0.4848)
2)
A) -31°
B) -28°
C) -29°
D) 151°
= sin-1 (0.6561)
A) 39°
B) 44°
C) -41°
D) 41°
1)
2)
Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
3) cos2 x - cos x = 0
3)
A)
5
+ 2n
3
B) 2n ,
2
+n
C)
2
+ 2n
D)
+ 2n }
Solve the equation for exact solutions.
4) arcsin y A)
6
=
4)
6
3+
6
B)
36
C)
Solve the equation for solutions in the interval [0, 2 ).
5) 2 3 sin 4x = 3
4
,
D)
6) sin 2x + sin x = 0
3 5
7
,
,
,
A)
4 4 4
4
C) 0,
D)
2
7 7
13 5 19
, ,
,
,
,
,
,
B)
12 6 3 12 6
12 3 12
A) {0}
C) 0,
3+
3
B)
2
4
, ,
3
3
4
,
5
4
6)
9
,
8 8
D)
Write the following as an algebraic expression in u, u > 0.
u2 + 4
7) sin arcsec
u
A)
u2 + 2
u2 + 2
5)
B)
7)
2 u2 + 4
u2 + 4
C) u 2
1
D)
u u2 + 2
u2 + 2
Provide an appropriate response.
8) True or false? The statement tan-1 (tan x) = x for all real numbers in the interval A) True
2
<x<
2
.
B) False
Give the degree measure of .
3
9) = cot-1
3
A) 60°
10)
9)
B) 300°
C) 30°
D) 120°
3
2
= cos-1
A) 315°
10)
B) 30°
C) 45°
D) 330°
Solve the equation for exact solutions.
1
=
11) sin-1 x + cos-1 2
A) -
3
3
,
4
4
11)
B) {1}
C)
3
2
D) {0}
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
12) sin 2 + sin = 0
A) {0°, 120°, 180°, 240°}
B) {105°, 165°, 285°, 345°}
C) {30°, 90°, 150°, 270°}
D) {15°, 165°, 195°, 345°}
Solve the equation for exact solutions over the interval [0, 2 ).
13) sin2 x + sin x = 0
5
A) 0, , ,
3 3
4 5
,
B) 0, ,
3 3
3
C) 0, ,
2
12)
2
D) 0, , ,
3 3
Write the following as an algebraic expression in u, u > 0.
u
14) sin arctan
5
A)
8)
u u2 - 5
u2 - 5
B)
13)
14)
u2 + 5
u2 + 5
C) u u2 + 5
D)
u u2 + 5
u2 + 5
Provide an appropriate response.
15) True or false? The statement tan(tan-1 x) = x for all real numbers in the interval -1 x 1.
A) True
B) False
Solve the equation for exact solutions.
15
16) cos-1 x = sin-1
17
A)
8
15
15)
16)
B) {0}
C)
2
8
17
D)
Use a calculator to give the value to the nearest degree.
17) = tan-1 (-0.7002)
A) -35°
B) -38°
C) 145°
D) -33°
Solve the problem.
18) Let (a, b) and (c, d) be two points in the first quadrant, and let be the angle between the line
segment connecting (a, b) with the origin and the line segment connecting (c, d) with the origin. It
can be shown that
ac + bd
cos =
.
2
a + b2 c2 + d2
17)
18)
Find if a = 7, b = 2, c = 3, and d = 6. Give your answer in degrees rounded to the nearest
hundredth.
A) 75.78°
B) 64.53°
C) 47.49°
D) 79.38°
Give the degree measure of .
1
19) = arcsin 2
A) 300°
Solve.
19)
B) 315°
C) 30°
D) -30°
20) Consider the formula T = 591 - 76 cos 2 , where is measured in degrees. To the nearest
hundredth of a degree, what is the smallest positive value of for which the value of T will be 525?
A) 11.86°
B) 32.72°
C) 29.72°
D) 14.86°
Use a calculator to give the real number value. Round the answer to 7 decimal places.
21) y = cos-1 (-0.3907)
A) 2.0079383
B) 1.9206367
C) -1.1698423
D) 1.9721882
Give the exact value of the expression.
1
22) cos arcsin
4
A)
15
2
20)
21)
22)
15
4
B)
C)
4 15
15
D)
2 15
15
Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
23) cot (-arcsin )
23)
A) -1094.771
B) 0
C) Undefined
D) -0.0009
Use a calculator to give the real number value. Round the answer to 7 decimal places.
24) y = tan-1 (0.5774)
A) 0.4714286
B) 1.0476200
Find the exact value of the real number y.
25) y = cot-1 (1)
A)
4
B)
4
3
C) 0.5236361
D) 0.5587302
5
C)
4
7
D)
4
24)
25)
Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
26) 2 sin2 x + sin x = 1
26)
A)
C)
6
2
+ 2n ,
5
+ 2n
6
B)
+ 2n ,
5
3
+ 2n ,
+ 2n
6
2
D)
6
6
+ 2n ,
5
3
+ 2n ,
+ 2n
6
2
+ 2n ,
3
+ 2n
2
Use a calculator to give the real number value. Round the answer to 7 decimal places.
27) y = cos-1 (-0.9397)
A) -0.3492063
B) 2.7925484
Use a calculator to give the value to the nearest degree.
28) = cos-1 (0.8910)
A) 29°
B) 27°
Find the exact value of the real number y.
29) y = arctan 1
3
A)
B)
3
4
C) 2.8285740
D) 2.7412723
C) 63°
D) 25°
D)
B) {0, }
2
7 7
13 5
, ,
,
,
,
,
12 6 3 12 6
12 3
D)
Solve the equation for exact solutions over the interval [0, 2 ).
31) csc5 x - 4 csc x = 0
C)
3
5
,
, ,
4 4 6 6
4
,
B)
3 5
7
,
,
4 4
4
D)
32) 2 sin2 x = sin x
5
,
A)
6 6
C)
2
4
30)
A) {0}
A)
28)
29)
2
C)
3
Solve the equation for solutions in the interval [0, 2 ).
30) tan 2x - tan x = 0
C)
27)
,
4
,
5
4
3
5
,
, ,
4 4 3 6
4
,
5
5
, ,
4 3 3
5
B) 0, , ,
6 6
3
2
, ,
2 3 3
D)
4
3
,
31)
2
3
32)
Solve the problem.
33) A painting 1 meter high and 3 meters from the floor will cut off an angle to an observer, where
x
, assuming that the observer is x feet from the wall where the painting is
= tan-1
2
x + 1.8
33)
displayed and that the eyes of the observer are 1.8 meters above the ground (see the figure). Find
the value of for x = 2. Round to the nearest tenth of a degree.
1.2
1.8
A) 19.0°
B) 27.8°
C) 16.5°
D) 21.5°
Provide an appropriate response.
34) True or false? The statement sin-1 (sin x) = x for all real numbers in the interval
A) True
B) False
x
.
34)
Solve the equation for solutions over the interval [0, 2 ). Write solutions as exact values or to four decimal places, as
appropriate.
x
x
35) sin + cos = 0
35)
2
2
A)
4
,
4
B)
C) {0 , }
2
D)
2
Give the exact value of the expression.
21
36) cot sin-1
35
A)
21
28
B)
36)
21
35
C)
28
21
D)
35
21
Solve the problem.
37) It can be shown that if the angle of elevation from an observer to the top of an object is A and the
angle of elevation d ft closer is B, then the height of the object is given by
d
h=
ft.
cot A - cot B
Find A if h = 90 ft, d = 80 ft, and B = 55°. Give your answer in degrees to the nearest hundredth.
A) 34.96°
B) 32.18°
C) 29.22°
D) 37.56°
5
37)
38) The range r of a projectile is given by
1 2
r=
v sin 2 ,
32
38)
where v is the initial velocity and is the angle of elevation. If r is to be 5000 ft and v = 5500 ft/sec,
what must the angle of elevation be? Give your answer in degrees to the nearest hundredth.
A) 0.15°
B) 0.21°
C) 0.30°
D) 89.85°
Give the degree measure of .
2
39) = sin-1
2
A) 45°
39)
B) 60°
C) 120°
D) 135°
Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
40) sin2 x + sin x = 0
40)
A)
C)
3
+n
2
B) n ,
+ 2n
D) n ,
2
3
+ 2n
2
2
+ 2n
Solve the problem.
41) A solar reflector is made using 40 identical triangular-shaped mirrors, each having sides
1.8 meters, 2 meters, 1.4 meters. What is the total surface area of the reflector (to the nearest square
meter)?
A) 49 m 2
B) 60 m 2
C) 43 m 2
D) 41 m 2
Find the missing parts of the triangle.
42) A = 29°
a = 35 km
b = 46 km
If necessary, round angles to the nearest whole number and side lengths to the nearest km.
A) no such triangle
B) B = 40°, C = 111°, c = 67 km
C) B1 = 111°, C1 = 40°, c1 = 67 km
B2 = 11°, C2 = 140°, c2 = 13 km
41)
42)
D) B1 = 40°, C1 = 111°, c1 = 67 km
B2 = 140°, C2 = 11°, c2 = 13 km
Draw a sketch to represent the vector. Refer to the vectors pictured here.
43) 3d
A)
B)
Solve the problem.
44) Lookout station B is located 14 mi due east of station A. The bearing of a fire from A is S10°20'W
and the bearing from B is S36°30'W. Determine the distance from the fire to B (to the nearest tenth
of a mile).
A) 33.2 mi
B) 31.2 mi
C) 15.6 mi
D) 17.6 mi
6
43)
44)
45) A guy wire to a tower makes a 65° angle with level ground. At a point 40 ft farther from the tower
than the wire but on the same side of the base as the wire, the angle of elevation to the top of the
pole is 40°. Find the wire length (to the nearest foot).
A) 66 ft
B) 127 ft
C) 61 ft
D) 122 ft
45)
46) Two people are carrying a box. One person exerts a force of 132 pounds at an angle of 40.4° with
the horizontal. The other person exerts a force of 98 pounds at an angle of 59.5°. Find the weight of
the box.
A) 230 lb
B) 266 lb
C) 118 lb
D) 177 lb
46)
47) If u = -5, 7 , v = -9, 6 , and w = -11, 2 , evaluate u · (v - w).
A) 18
B) 13
C) 45
47)
D) 22
Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
48) b = 12.1 ft
A = 17°10'
C = 102°50'
A) 48.6 ft2
B) 53.6 ft2
C) 19.3 ft2
D) 24.3 ft2
49) a = 151 m
b = 163 m
c = 173 m
A) 11,306 m 2
48)
49)
B) 14,133 m 2
C) 725 m 2
Determine whether the pair of vectors is orthogonal.
50) 5, 3 , -2 3, 10
A) Yes
D) 16,959 m 2
B) No
50)
Draw a sketch to represent the vector. Refer to the vectors pictured here.
51) b - c
A)
B)
Find the missing parts of the triangle.
52) B = 105.8°
a = 298 cm
b = 1294 cm
If necessary, round angles the nearest tenth and side lengths to the nearest cm.
A) A = 12.8°, C = 61.4°, c = 1181 cm
B) A = 15.8°, C = 58.4°, c = 1181 cm
C) A = 61.4°, C = 12.8°, c = 1181 cm
D) no such triangle
Solve the problem.
53) Find the area of a triangular garden if the sides are approximately 5 feet, 8 feet, and 12 feet (to the
nearest square foot).
A) 4 ft2
B) 240 ft2
C) 15 ft2
D) 331 ft2
7
51)
52)
53)
Use the figure to find the specified vector.
54) Find -a.
A) 8, -6
54)
B) 6, -8
C) -6, -8
D) -8, 6
Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
55) -12, 5
55)
A) 15; 157.4°
B) 13; 22.6°
C) 13; 112.6°
D) 13; 157.4°
Vector v has the given magnitude and direction. Find the magnitude of the indicated component of v rounded to the
nearest tenth when necessary.
56) = 39.4°, v = 206; Find the vertical component of v.
56)
A) 159.2
B) 290
C) 130.8
D) 28.4
Find the indicated vector.
57) Let a = 3i, b = i + j. Find 6a + b.
A) 19i + 6j
B) 19i + j
C) i + 19j
D) 11i + j
57)
Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant
force.
58) forces of 43 and 60 newtons, forming an angle of 90°
58)
(round to the nearest newton)
A) 103 newtons
B) 2580 newtons
C) 17 newtons
D) 74 newtons
Solve the problem.
59) Two forces, of 43.2 and 32.5 lb, forming an angle of 130.6°, act at a point in the plane. Find the
magnitude of the resultant force.
A) 1100 lb
B) 68.9 lb
C) 33.1 lb
D) 75.7 lb
59)
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
60) C = 122°
60)
a = 6.3 m
b = 10.2 m
A) No triangle satisfies the given conditions.
B) c = 20.4 m, A = 19.3°, B = 38.7°
C) c = 14.6 m, A = 21.3°, B = 36.7°
D) c = 17.5 m, A = 23.3°, B = 34.7°
8
Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
61) sin (arctan 2)
61)
A) 0.8944
B) 0
C) Undefined
D) -0.8172
Graph the inverse circular function.
62) y = sin-1 x
62)
A)
B)
C)
D)
Solve the problem.
63) A generator produces an alternating current according to the equation I = 8 sin 124 t, where t is
time in seconds and I is the current in amperes. What is the smallest time t such that I = 4?
1
1
1
1
sec
sec
sec
sec
A)
B)
C)
D)
248
372
744
496
9
63)
Use a calculator to give the real number value. Round the answer to 7 decimal places.
64) y = sin-1 (-0.4848)
A) -0.5412698
B) 2.6365103
C) -0.4888889
D) -0.5061345
Solve the equation for solutions in the interval [0, 2 ).
65) sin2 2x = 1
A)
65)
9
,
8 8
C) 0,
B)
2
4
, ,
3
3
D)
4
,
3 5
7
,
,
4 4
4
Find the exact value of the real number y.
2
66) y = arccos
2
A) -
B)
3
66)
C)
4
3
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
67) tan2 2 = 5
A) {0°}
B) {33°, 57°, 123°, 147°, 213°, 237°, 303°, 327°}
C) {0°, 90°, 180°, 270°}
D) {0°, 45°, 90°, 135°, 180°, 225°, 270°}
68) sin 2 = -
64)
1
2
D)
3
4
67)
68)
A) {105°, 165°, 285°, 345°}
C) {0°, 120°, 180°, 240°}
B) {30°, 90°, 150°, 270°}
D) {15°, 165°, 195°, 345°}
Graph the inverse circular function.
1
69) y = arccot x
2
69)
10
A)
B)
C)
D)
Write the following as an algebraic expression in u, u > 0.
70) sin(arctan u)
u u2 - 1
u2 + 1
A)
B)
u2 - 1
u2 + 1
Sketch the vectors u and w with angle
71) u = 50, w = 12, = 35°
A)
70)
C)
u u2 + 1
u2 + 1
D) u u2 + 1
between them and sketch the resultant.
B)
Solve the problem.
72) A plane is heading due south with an airspeed of 214 mph. A wind from a direction of 56° is
blowing at 11 mph. Find the bearing of the plane.
A) 177°
B) 88°
C) 93°
D) 182°
11
71)
72)
Sketch the vectors u and w with angle
73) u = 8, w = 16, = 15°
A)
between them and sketch the resultant.
73)
B)
Determine whether the pair of vectors is orthogonal.
74) 2, -1 , 16, 32
A) Yes
74)
B) No
Find the missing parts of the triangle.
75) A = 74°
a = 38 yd
b = 77 yd
If necessary, round angles to the nearest degree and side lengths to the nearest yard.
A) B = 77°, C = 29°, c = 79 yd
B) no such triangle
C) B = 29°, C = 77°, c = 75 yd
D) B = 29°, C = 77°, c = 81 yd
Solve.
76) A coil of wire rotating in a magnetic field induces a voltage given by e = 20 sin
75)
t
, where t is
4
2
76)
time in seconds. Find the smallest positive time to produce a voltage of 10 2. Round values to the
nearest hundredth.
A) 3 sec
B) 2.8 sec
C) 3 sec
D) 2.8 sec
Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
77) sin 2 = -sin
A) {60°, 120°, 240°, 300°}
B) {0°, 60°, 120°, 180°, 240°, 300°}
C) {0°, 120°, 180°, 240°}
D) {0°, 180°}
77)
Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
78)
78)
A) 180.3 lb
B) 132.7 lb
C) 21,459.5 lb
D) 146.5 lb
Find the exact value of the real number y.
1
79) y = arcsin
2
A)
B)
79)
C)
3
12
6
D)
7
6
Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
80)
A) 4.7, 1.82
B) 4.7, 1.71
C) 1.71, 4.7
13
80)
D) 0.94, 0.34
Answer Key
Testname: PRACTICETEST3TRIG
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
C
D
B
A
B
C
B
B
A
B
C
A
C
D
A
C
A
C
D
D
D
B
C
C
B
B
B
B
D
B
C
B
A
A
D
C
B
A
A
B
A
D
B
B
C
D
A
D
A
A
14
Answer Key
Testname: PRACTICETEST3TRIG
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
B
A
C
B
D
C
B
D
C
C
A
C
C
D
D
B
B
A
B
C
B
D
A
A
B
C
C
D
C
B
15