Download trig final.tst

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Tell in which quadrant or on what coordinate axis the point lies.
1) (5, -19)
A) Quadrant II
B) Quadrant III
C) Quadrant I
1)
D) Quadrant IV
Find the distance d(P1 , P2 ) between the points P1 and P2 .
2) P1 = (6, 2); P2 = (-5, -6)
A) 185
2)
B) 3
C)
57
D) 88
Solve the problem.
3) Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10.
A) (9, -12), (9, 8)
B) (9, 13), (9, -7)
C) (9, 2), (9, -4)
D) (9, 6), (9, -10)
List the intercepts of the graph.
4)
3)
4)
y
5
4
3
2
1
-π
-π
2
-1
π
2
π
x
-2
-3
-4
-5
π
π
A) - , 0 , (2, 0), , 0
2
2
B) 0, - π
π
, (0, 2), 0, 2
2
π
π
C) - , 0 , (0, 2), , 0
2
2
D) 0, - π
π
, (2, 0), 0, 2
2
List the intercepts for the graph of the equation.
5) y = x2 + 8x + 16
5)
B) (0, 4), (0, 4), (16, 0)
D) (4, 0), (4, 0), (0, 16)
A) (0, -4), (0, -4), (16, 0)
C) (-4, 0), (-4, 0), (0, 16)
1
Determine whether the graph of the equation is symmetric with respect to the x -axis, the y-axis, and/or the origin.
3x
6)
6) y = 2
x + 9
A) x-axis
B) y-axis
C) origin
D) x-axis, y-axis, origin
E) none
Solve the problem.
7) Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a
diameter.
A) (x + 1)2 + (y + 1)2 = 34
B) (x - 1)2 + (y - 1)2 = 34
7)
D) (x - 1)2 + (y - 1)2 = 136
C) (x + 1)2 + (y + 1)2 = 136
Determine whether the relation represents a function. If it is a function, state the domain and range.
8)
Alice
snake
Brad
cat
Carl
dog
A) function
domain: {Alice, Brad, Carl}
range: {snake, cat, dog}
B) function
domain: {snake, cat, dog}
range: {Alice, Brad, Carl}
C) not a function
9) {(-2, 3), (-1, 0), (0, -1), (1, 0), (3, 8)}
A) function
B) function
domain: {3, 0, -1, 8}
domain: {-2, -1, 0, 1, 3}
range: {-2, -1, 0, 1, 3}
range: {3, 0, -1, 8}
8)
9)
C) not a function
Find the value for the function.
10) Find f(3) when f(x) = x2 + 5x.
B)
A) 2 6
10)
30
C)
14
D)
34
Find the domain of the function.
x - 4
11) h(x) = x3 - 25x
11)
B) {x|x ≠ -5, 0, 5}
D) all real numbers
A) {x|x ≠ 0}
C) {x|x ≠ 4}
12) f(x) = 7 - x
A) {x|x ≠ 7}
12)
B) {x|x ≠ 7}
C) {x|x ≤ 7}
2
D) {x|x ≤ 7}
Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if
any, and any symmetry with respect to the x -axis, the y-axis, or the origin.
13)
13)
y
1
-π
-3π -π
4 2
-π
4
π
4
π
2
3π
4
π
x
-1
A) function
domain: {x|-π ≤ x ≤ π}
range: {y|-1 ≤ y ≤ 1}
π
π
π
π
3π
3π
3π
, 0), (- , 0), (- , 0), (0, 0), ( , 0), ( , 0), (
, 0), (
, 0), (π, 0)
intercepts: (-π, 0), (- 2
4
4
2
4
4
4
symmetry: origin
B) function
domain: all real numbers
range: {y|-1 ≤ y ≤ 1}
π
π
π
π
3π
3π
3π
, 0), (- , 0), (- , 0), (0, 0), ( , 0), ( , 0), (
, 0), (
, 0), (π, 0)
intercepts: (-π, 0), (- 2
4
4
2
4
4
4
symmetry: origin
C) function
domain: {x|-1 ≤ x ≤ 1}
range: {y|-π ≤ y ≤ π}
π
π
π
π
3π
3π
3π
, 0), (- , 0), (- , 0), (0, 0), ( , 0), ( , 0), (
, 0), (
, 0), (π, 0)
intercepts: (-π, 0), (- 2
4
4
2
4
4
4
symmetry: none
D) not a function
Answer the question about the given function.
12
x2 - 8
, is the point (2, ) on the graph of f?
14) Given the function f(x) = 5
x + 3
A) Yes
14)
B) No
Determine algebraically whether the function is even, odd, or neither.
x
15) f(x) = x2 + 4
A) even
B) odd
15)
C) neither
3
The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
16)
16) (-1, 0)
3
y
2
1
-2
-1
1
2
x
-1
-2
-3
A) increasing
B) constant
C) decreasing
Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
17) f(x) = x3 - 3x2 + 3, (-1, 3)
17)
A) local maximum at (2, -1)
local minimum at (0, 3)
increasing on (-1, 0)
decreasing on (0, 2)
C) local maximum at (2, -1)
local minimum at (0, 3)
increasing on (-1, 0) and (2, 3)
decreasing on (0, 2)
B) local maximum at (0, 3)
local minimum at (2, -1)
increasing on (-1, 0) and (2, 3)
decreasing on (0, 2)
D) local maximum at (0, 3)
local minimum at (2, -1)
increasing on (0, 2)
decreasing on (-1, 0) and (2, 3)
Using transformations, sketch the graph of the requested function.
18) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the
function F(x), where F(x) = f(x + 2) - 1.
y
5
(-1, 1)
-5
5
x
(-3, -2)
(3, -4)
-5
4
18)
A)
B)
y
y
5
5
(-3, 2)
(-3, 1)
-5
5
x
-5 (-5, -1)
5
x
5
x
(-5, -2)
(1, -3)
(1, -4)
-5
-5
C)
D)
y
y
5
5
(-3, 0)
(1, 0)
-5
5
x
-5
(-1, -3)
(-5, -3)
-5
-5
(1, -5)
Convert the angle to a decimal in degrees. Round the answer to two decimal places.
19) 42°55ʹ18ʹʹ
A) 42.93°
B) 42.92°
C) 42.98°
20) 83°13ʹ2ʹʹ
A) 83.18°
(5, -5)
19)
D) 42.88°
20)
B) 83.22°
C) 83.23°
D) 83.28°
If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
1
21)
21) r = feet, s = 7 feet, θ = ?
2
A)
7
°
2
B)
7
radians
2
C) 14 radians
Convert the angle in degrees to radians. Express the answer as multiple of π.
22) 75°
6π
4π
5π
A)
B)
C)
13
11
12
5
D) 14°
22)
12π
D)
5
Solve the problem.
23) The Earth rotates about its pole once every 24 hours. The distance from the pole to a location on
Earth 49° north latitude is about 2598 miles. Therefore, a location on Earth at 49° north latitude is
spinning on a circle of radius 2598 miles. Compute the linear speed on the surface of the Earth at
49° north latitude.
A) 680 mph
B) 108 mph
C) 628 mph
D) 16,324 mph
23)
In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value
of the indicated trigonometric function of t.
3
55
24) ( , )
Find tan t.
24)
8 8
A)
8
3
B)
55
8
55
3
C)
D)
3 55
55
Find the exact value. Do not use a calculator.
π
25) sin (- )
2
25)
B) -1
A) 1
C) 0
D) undefined
Find the exact value of the expression if θ = 45°. Do not use a calculator.
26) g(θ) = sin θ
Find [g(θ)]2 .
A)
1
2
B) - 2
2
C)
2
26)
D) 2
Find the exact value of the expression. Do not use a calculator.
π
π
27) sin - cos 3
6
A) 0
B)
3 - 1
2
27)
C)
3
Find the exact value of the expression if θ = 30°. Do not use a calculator.
28) g(θ) = cos θ
Find g(2θ).
1
C) 3
A) 1
B)
2
D) 1
28)
3
D)
2
Find the exact value of the expression. Do not use a calculator.
π
5π
29) cos + tan 3
3
A)
3 + 1
2
B)
2 3 + 3
6
29)
C)
1 - 2 3
2
D)
3 + 3
3
A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
30) (-5, -12)
Find cos θ.
30)
5
12
5
12
A) - B)
C)
D) - 13
13
13
13
6
Solve the problem.
31) For what numbers θ is f(θ) = tan θ not defined?
π
A) odd multiples of (90°)
2
31)
B) all real numbers
C) integral multiples of π (180°)
D) odd multiples of π (180°)
Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a
calculator.
32) cot 570°
32)
3
3
A)
B) - C) - 3
D) 3
3
3
33) sin 11π
3
33)
3
2
A) - B) - 1
2
3
2
C)
Name the quadrant in which the angle θ lies.
34) sin θ > 0,
cos θ < 0
A) I
B) II
D) -1
34)
C) III
D) IV
In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function.
1
15
35) sin θ = , cos θ = Find csc θ.
4
4
A) 4
B)
15
C)
4 15
15
D)
15
15
Find the exact value of the indicated trigonometric function of θ.
8
3π
36) cos θ = , < θ < 2π
Find cot θ.
17
2
A) - 15
8
B) - 8
15
C) - 36)
8
3
D)
17
8
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
37) sin (-120°)
3
1
3
-1
A)
B)
C)
D) - 2
2
2
2
Without graphing the function, determine its amplitude or period as requested.
38) y = -2 sin x
Find the amplitude.
π
B) 2
C) -2π
A)
2
39) y = sin 3x
A) 2π
35)
37)
38)
D) 2π
Find the period.
39)
B) 1
C) 3
7
2π
D)
3
Answer the question.
40) Which one of the equations below matches the graph?
A) y = 3 cos 4x
B) y = 3 cos
1
x
4
40)
C) y = -3 sin 4x
D) y = 3 sin
1
x
4
Find an equation for the graph.
41)
41)
y
5
4
3
2
1
-2π
-π
π
-1
2π
x
-2
-3
-4
-5
A) y = 2 cos 1
x
3
B) y = 2 cos (3x)
C) y = 3 cos (2x)
D) y = 3 cos 1
x
2
Solve the problem.
1
42) For the equation y = - cos(2x - 2π), identify (i) the amplitude, (ii) the phase shift, and (iii) the
2
42)
period.
A) (i) 1
2
(ii) π
(iii) π
B) (i) 2
(ii) 2π
(iii) 2π
C) (i) 1
2
(ii) π
2
(iii) π
D) (i) 2
(ii) π
(iii) π
Find the exact value of the expression.
3
43) cos-1 - 2
A)
π
6
B)
43)
π
3
C)
8
5π
6
D)
2π
3
3
44) tan-1 3
A)
44)
7π
6
B)
π
3
C)
π
4
D)
π
6
Find the exact value of the expression. Do not use a calculator.
45) sin [sin-1 (0.2)]
A) 5
B) 0.2
D) 5.0335
5π
7
46) sin-1 sin A)
45)
C) 0.8
7
5π
46)
B)
5π
7
C)
2π
7
D)
7
2π
Use a calculator to find the value of the expression rounded to two decimal places.
1
47) sin-1 8
A) 82.82
B) 7.18
C) 0.13
47)
D) 1.45
Find the exact solution of the equation.
48) 2 cos-1 x = π
48)
π
C) x = 2
3π
B) x = 2
A) x = 0
D) x = 1
Find the exact value of the expression.
49) sin (tan-1 2)
A) 5 2
50) cos sin-1 A) - 49)
2 5
B)
5
5 2
C)
2
D) 2 5
4
5
3
5
50)
B) - 4
5
C)
1
5
D)
3
5
51) cot-1 - 3
π
A)
6
5π
B)
6
π
C)
3
2π
D)
3
52) sec -1 (-2)
2π
A) - 3
4π
B)
3
2π
C)
3
π
D) - 3
51)
52)
Use a calculator to find the value of the expression in radian measure rounded to two decimal places.
53) cot-1 5
A) 1.37
B) 11.31
C) 78.69
9
D) 0.20
53)
Complete the identity.
54)
(sin θ + cos θ)2
= ?
1 + 2 sin θ cos θ
A) 1 - sin θ
55) cos θ - cos θ sin2 θ = ?
A) sec 2 θ
54)
B) -sec 2 θ
C) 1
B) cos3 θ
C) tan2 θ
D) 0
55)
D) sin θ
Find the exact value of the expression.
11π
56) sin - 12
6 + 2
4
A) - 56)
2 - 6
4
B)
C)
Find the exact value under the given conditions.
21
π
12
π
57) sin α = , 0 < α < ; cos β = , 0 < β < 29
2
13
2
A)
345
377
58) tan α = A)
B)
B)
6 - 2
4
D)
Find cos (α + β).
152
377
C)
7
3π
12 π
, π < α < ; cos β = - , < β < π
24
2
13 2
253
325
2 + 6
4
135
377
57)
D)
352
377
Find sin (α + β).
204
325
C)
323
325
58)
D) - 36
325
Find the exact value of the expression.
4
3
59) cos tan-1 - sin-1 3
5
A)
2 3
5
B)
59)
2 6
5
C)
24
25
D) 1
Use the information given about the angle θ, 0 ≤ θ ≤ 2π, to find the exact value of the indicated trigonometric function.
15 3π
60) cos θ = , < θ < 2π
Find sin (2θ).
60)
17
2
A) - 161
289
B)
161
289
3
61) csc θ = - , tan θ > 0
2
A)
1
9
5
5
240
289
D) - 240
289
Find cos (2θ).
B) - 3
3π
62) cos θ = - , π < θ < 5
2
A)
C)
61)
1
9
C)
-4 5
9
D)
4 5
9
θ
Find cos .
2
B) - 62)
5
5
C)
10
30
10
D) - 30
10
3 3π
63) sin θ = - , < θ < 2π
5
2
A) - 30
10
θ
Find sin .
2
B) - 63)
10
10
5
5
C)
D) - 5
5
Express the product as a sum containing only sines or cosines.
64) sin (5θ) cos (2θ)
1
B) sin cos (10θ2 )
A) [sin (7θ) + sin (3θ)]
2
C)
1
[sin (7θ) + cos (3θ)]
2
D)
64)
1
[cos (7θ) - cos (3θ)]
2
Express the sum or difference as a product of sines and/or cosines.
65) cos (6θ) + cos (4θ)
A) 2 cos (5θ)
B) 2 cos (5θ) sin θ
C) 2 sin (5θ) sin θ
65)
D) 2 cos (5θ) cos θ
Solve the equation on the interval 0 ≤ θ < 2π.
3
66) sin (4θ) = 2
A)
66)
π 5π
, 4 4
B) 0
π
C) 0, , π
4
D)
π π 2π 7π 7π 13π 5π 19π
, , , , , , , 12 6 3 12 6
12
3
12
Solve the equation. Give a general formula for all the solutions.
2
67) cos (2θ) = 2
π
7π
A) θ = + 2kπ, θ = + 2kπ
8
8
C) θ = 67)
π
7π
B) θ = + kπ, θ = + kπ
8
8
4π
2π
+ kπ, θ = + kπ
3
3
π
3π
D) θ = + kπ, θ = + kπ
4
4
Solve the equation on the interval 0 ≤ θ < 2π.
68) 2 sin2 θ = sin θ
π 5π
A) , 6 6
68)
π 3π π 2π
B) , , , 2 2 3 3
π 2π
C) , 3 3
69) sin2 θ - cos2 θ = 0
π π
A) , 4 6
C)
π 5π
D) 0, π, , 6 6
69)
π π
B) , 4 3
π 3π 5π 7π
, , , 4 4
4
4
D)
11
π
4
Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.
70)
70) Find sin B when b = 3 and c = 4.
3 7
7
4 7
3
B)
C)
D)
A)
7
4
7
4
Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
71) a = 5, b = 6; Find c, α, and β.
A) c = 7.81
B) c = 5.57
α = 39.81°
α = 39.81°
β = 50.19°
β = 50.19°
71)
C) c = 7.81
α = 40.81°
β = 49.19°
Solve the triangle.
γ = 60°,
b = 4
72) β = 70°,
A) α = 50°, c = 3.69, a = 3.26
C) α = 50°, c = 3.26, a = 3.69
D) c = 5.57
α = 40.81°
β = 49.19°
72)
B) α = 50°, c = 3.26, a = 2.69
D) α = 50°, c = 4.69, a = 3.26
Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.
73) a = 7, b = 9, β = 49°
73)
A) one triangle
B) one triangle
α = 76.01°, γ = 54.99°, c = 7.60
α = 35.94°, γ = 95.06°, c = 11.88
C) two triangles
α1 = 76.01°, γ1 = 54.99°, c1 = 7.60 or
D) no triangle
α2 = 103.99°, γ2 = 27.01, c2 = 12.14
74) a = 12, b = 8, β = 10°
A) two triangles
α1 = 15.1°, γ1 = 154.9°, c1 = 19.54 or
74)
B) one triangle
α = 164.9°, γ = 5.1°, c = 4.1
α2 = 164.9°, γ2 = 5.1°, c2 = 4.1
C) one triangle
α = 15.1°, γ = 154.9°, c = 19.54
D) no triangle
Solve the triangle.
75) b = 5, c = 6, α = 80°
A) a = 8.11, β = 43.8°, γ = 56.2°
C) a = 7.11, β = 43.8°, γ = 56.2°
75)
B) a = 6.11, β = 56.2°, γ = 43.8°
D) a = 7.11, β = 56.2°, γ = 43.8°
12
Solve the triangle. Find the angles α and β first.
76) a = 7, b = 13, c = 17
A) α = 20.3°, β = 44.8°, γ = 114.9°
C) α = 24.3°, β = 42.8°, γ = 112.9°
76)
B) α = 22.3°, β = 44.8°, γ = 112.9°
D) no triangle
Find the area of the triangle. If necessary, round the answer to two decimal places.
77) α = 30°, b = 12, c = 6
A) 18
B) 33.18
C) 16
78) a = 14, b = 32, c = 26
A) 181.99
77)
D) 31.18
78)
B) 5280.01
C) 3219.69
D) 177.99
Match the point in polar coordinates with either A, B, C, or D on the graph.
π
79) -3, 3
79)
5
4
A
3
B
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 r
-1
-2
D
-3
C
-4
-5
A) A
B) B
C) C
D) D
The polar coordinates of a point are given. Find the rectangular coordinates of the point.
2π
80) 7, 3
7 7 3
A) - , 2
2
B)
7 -7 3
, 2
2
C)
7 7 3
, 2
2
The rectangular coordinates of a point are given. Find polar coordinates for the point.
81) (-2, 2)
3π
3π
3π
A) 2 2, B) -2 2, C) 2 2,
4
4
4
80)
7 -7 3
D) - , 2
2
81)
π
D) -2 2,
4
Write the complex number in polar form . Express the argument in degrees, rounded to the nearest tenth, if necessary.
82) 3 - i
82)
A) 4(cos 330° + i sin 330°)
B) 4(cos 300° + i sin 300°)
C) 2(cos 300° + i sin 300°)
D) 2(cos 330° + i sin 330°)
13
Solve the problem. Leave your answer in polar form.
83) z = 10(cos 45° + i sin 45°)
w = 5(cos 15° + i sin 15°)
Find zw.
A) 5(cos 60° + i sin 60°)
C) 50(cos 30° + i sin 30°)
83)
B) 50(cos 60° + i sin 60°)
D) 5(cos 30° + i sin 30°)
Write the expression in the standard form a + bi.
5π
5π 4
84) 3 cos + i sin 6
6
A) - 9 3 9
+ i
2
2
84)
9 9 3
B) - - i
2
2
9 9 3
C) - + i
2
2
D) - 9 3 9
- i
2
2
Find all the complex roots. Leave your answers in polar form with the argument in degrees.
85) The complex fourth roots of -16
4
4
4
4
A) 2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 2(cos 315° + i sin
315°)
B) 2(cos 90° + i sin 90°), 2(cos 180° + i sin 180°), 2(cos 270° + i sin 270°), 2(cos 360° + i sin 360°)
C) 16(cos 45° + i sin 45°), 16(cos 135° + i sin 135°), 16(cos 225° + i sin 225°), 16(cos 315° + i sin
315°)
D) 2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 16(cos 315° + i sin 315°)
85)
The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.
86) P = (5, 4); Q = (-1, -3)
86)
A) v = 7i + 6j
B) v = 6i + 7j
C) v = -6i - 7j
D) v = -7i - 6j
Solve the problem.
87) If u = -10i - 2j and v = -2i + 7j, find u - v.
A) -9i + 5j
B) -10i + 5j
88) If v = 6i - 8j, find v .
A) 14
87)
C) -12i + 5j
D) -8i - 9j
88)
B) 100
C) 10
D)
10
Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis.
89) v = 15, α = 210°
89)
15 3
1
15
15 3
A) v = 15 - i - B) v = 15 - j
i - j
2
2
2
2
C) v = 15 - 2
2
i - j
2
2
D) v = 15
14
15
15 3
i - j
2
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
90) An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two
cables as shown in the figure. To two decimal places, what is the tension in the two
cables?
90)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the dot product v · w.
91) v = 12i + 4j,
w = -12i - 4j
A) -128
B) -144
91)
C) -160
D) -16
Find the angle between v and w. Round your answer to one decimal place, if necessary.
92) v = -5i + 7j,
w = -6i - 4j
A) 90.9°
B) 88.2°
C) 110.8°
D) 20.7°
92)
Solve the problem.
93) Which of the following vectors is parallel to v = -10i - 8j?
A) w = 20i + 16j
B) w = 3i - 5j
C) w = -20i + 25j
93)
State whether the vectors are parallel, orthogonal, or neither.
94) v = 3i + 4j,
w = 6i + 8j
A) Parallel
B) Orthogonal
95) v = 4i + j,
w = i - 4j
A) Orthogonal
D) w = 4i + 4j
94)
C) Neither
95)
B) Parallel
C) Neither
Solve the problem. Round your answer to the nearest tenth.
96) A wagon is pulled horizontally by exerting a force of 60 pounds on the handle at an angle of 25 ° to
the horizontal. How much work is done in moving the wagon 50 feet? ʺ .
A) 2718.9 ft-lb
B) 2110.8 ft-lb
C) 1617.4 ft-lb
D) 1267.9 ft-lb
15
96)
Answer Key
Testname: TRIG FINAL
1) D
2) A
3) D
4) C
5) C
6) C
7) B
8) C
9) B
10) A
11) B
12) C
13) A
14) B
15) B
16) C
17) B
18) C
19) B
20) B
21) C
22) C
23) A
24) C
25) B
26) A
27) A
28) B
29) C
30) A
31) A
32) D
33) A
34) B
35) A
36) B
37) D
38) B
39) D
40) B
41) D
42) A
43) C
44) D
45) B
46) C
47) C
48) A
49) B
50) D
16
Answer Key
Testname: TRIG FINAL
51) B
52) C
53) D
54) C
55) B
56) B
57) C
58) D
59) C
60) D
61) A
62) B
63) B
64) A
65) D
66) D
67) B
68) D
69) C
70) A
71) A
72) A
73) B
74) A
75) C
76) B
77) A
78) D
79) D
80) A
81) C
82) D
83) B
84) B
85) D
86) C
87) D
88) C
89) B
90) Tension in right cable: 35.90 lb; tension in left cable: 41.59 lb
91) C
92) B
93) A
94) A
95) A
96) A
17