Question 1
Find the exact value of the expression. Do not use a calculator.
sin - cos
Question 1 options:
1
0
Question 2
Use transformations to graph the function.
y = 5 sin (π - x)
Question 2 options:
Question 3
Write the equation of a sine function that has the given characteristics.
Amplitude: 4
Period: 3π
Phase Shift: -
Question 3 options:
y = 4 sin
y = 4 sin
y = 4 sin
y = 4 sin
Question 4
Find the exact value of the expression.
cos
Question 4 options:
-
-
Question 5
Solve the equation on the interval 0 ≤ θ < 2π.
4 cos2x - 3 = 0
Question 5 options:
Question 6
Use the information given about the angle θ, 0 ≤ θ ≤ 2π, to find the exact value of the indicated trigonometric function.
sin θ = , 0 < θ < Find sin .
Question 6 options:
Question 7
Express the product as a sum containing only sines or cosines.
cos(4θ) cos(3θ)
Question 7 options:
[ cos θ + cos(7θ)]
cos2(12θ2)
[cos(7θ) - sin θ]
[cos(7θ) - cos θ]
Question 8
Express the sum or difference as a product of sines and/or cosines.
sin(9θ) - sin(3θ)
Question 8 options:
2 sin(3θ)
2 sin(6θ) cos(3θ)
2 cos(3θ) cos(6θ)
2 sin(3θ) cos(6θ)
Question 9
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up.
a = 16; T = 8 seconds
Question 9 options:
d = -8 cos
d = -16 cos
d = -16 cos
d = -16 sin
Question 10
The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency?
d = 8 - 5 sin (πt)
Question 10 options:
simple harmonic; -5 m; 2 sec; oscillation/sec
simple harmonic; 5 m; sec; 2 oscillations/sec
simple harmonic; 8 m; 2 sec; oscillation/sec
simple harmonic; 5 m; 2 sec; oscillation/sec
Question 11
Match the point in polar coordinates with either A, B, C, or D on the graph.
Question 11 options:
A
B
C
D
Question 12
The polar coordinates of a point are given. Find the rectangular coordinates of the point.
Question 12 options:
Question 13
The rectangular coordinates of a point are given. Find polar coordinates for the point.
(-4, 0)
Question 13 options:
(4, π)
(-4, π)
Question 14
The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).
2xy = 3
Question 14 options:
2r cos θ sin θ = 3
r2 cos θ sin θ = 6
r2 sin 2θ = 6
r2 sin 2θ = 3
Question 15
The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
r = 1 + 2 sin θ
Question 15 options:
= x2 + y2 + 2y
x2 + y2 = + 2y
= x2 + y2 + 2x
x2 + y2 = + 2x
Question 16
The polar equation of the graph is either r = a + b cos θ or r = a + b sin θ, a > 0, b > 0. Match the graph to one of the equations.
Question 16 options:
r = 2 + 4 sin θ
r = 2 + 4 cos θ
r = 4 + 2 cos θ
r = 4 + 2 sin θ
Question 17
Identify and graph the polar equation.
r = 5 + 4 sin θ
Question 17 options:
limacon with inner loop
limacon with inner loop
limacon without inner loop
limacon without inner loop
Question 18
Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary.
2
Question 18 options:
2(cos 0° + i sin 0°)
2(cos 90° + i sin 90°)
2(cos 180° + i sin 180°)
2(cos 270° + i sin 270°)
Question 19
Write the complex number in rectangular form.
3
Question 19 options:
+ i
+ i
+ i
+ i
Question 20
Write the expression in the standard form a + bi.
4
Question 20 options:
- + i
- - i
- + i
- - i
Question 21
Find the dot product v ∙ w.
v = i - 7j, w = i - j
Question 21 options:
- 7
-12
12
+ 7
Question 22
State whether the vectors are parallel, orthogonal, or neither.
v = 2i + j, w = i - 2j
Question 22 options:
Parallel
Orthogonal
Neither
Question 23
Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.
v = -3i + 5j, w = 2i + j
Question 23 options:
v1 = - i - j, v2 = - i + j
v1 = - i - j, v2 = - i + j
v1 = - i - j, v2 = - i + j
v1 = - i - j, v2 = i + j
Question 24
Graph the curve whose parametric equations are given.
x = 4 tan t, y = 5 sec t; 0 ≤ t ≤ 2π
Question 24 options:
Question 25
Find two sets of parametric equations for the given rectangular equation.
y = 5x + 7
Question 25 options:
x = t, y = 5t + 7; x = , y = t + 7
x = t, y = 5t + 7; x = 5t, y = t + 7
x = t, y = 5t + 7; x = t, y = + 7
x = 5t, y = t + 7; x = , y = t + 7
If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
r = 15.0 inches, θ = 30°, s = ?
Question 1 options:
7.9 in.
8.2 in.
8.1 in.
8.0 in.
Question 2
A wheel of radius 1.9 feet is moving forward at 12 feet per second. How fast is the wheel rotating?
Question 2 options:
3.8 radians/sec
0.16 radians/sec
1.65 radians/sec
6.3 radians/sec
Question 3
Find the exact value of the indicated trigonometric function of θ.
cos θ = , tan θ < 0 Find sin θ.
Question 3 options:
-
-
-
-
Question 4
Graph the function.
y = - sec (πx)
Question 4 options:
Question 5
Write the trigonometric expression as an algebraic expression in u.
sin (tan-1 u)
Question 5 options:
u
Question 6
Find the exact value under the given conditions.
cos α = - , < α < π; sin β = , < α < π Find tan(α + β).
Question 6 options:
-
-
-
Question 7
Find the value of the indicated trigonometric function of the angle θ in the figure. Give an exact answer with a rational denominator.
Find csc θ.
Question 7 options:
csc θ =
csc θ =
csc θ =
csc θ =
Question 8
Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
b = 5, A = 30°; Find a, c, and B.
Question 8 options:
a = 3.89
c = 6.78
B = 60°
a = 2.89
c = 5.78
B = 60°
a = 3.89
c = 5.78
B = 60°
a = 2.89
c = 6.78
B =60°
Question 9
A building 210 feet tall casts a 50 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)
Question 9 options:
14°
77°
76°
13°
Question 10
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.
a = 5, b = 4, B = 15°
Question 10 options:
two triangles
A1 = 18.88°, C1 = 146.12°, c1 = 8.62 or
A2 = 161.12°, C2 = 3.88°, c2 = 1.05
one triangle
A = 161.12°, C = 3.88°, c = 1.05
one triangle
A = 18.88°, C = 146.12°, c = 8.62
no triangle
Question 11
A surveyor standing 68 meters from the base of a building measures the angle to the top of the building and finds it to be 36°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 50°. How tall is the radio tower?
Question 11 options:
11.3 m
31.63 m
12.12 m
16.95 m
Question 12
Solve the triangle.
a = 8, c = 6, B = 90°
Question 12 options:
b = 10, A = 36.9°, C = 53.1°
b = 10, A = 53.1°, C = 36.9°
b = 11, A = 53.1°, C = 36.9°
b = 9, A = 36.9°, C = 53.1°
Question 13
A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, how tall is the ladder to the nearest foot?
Question 13 options:
58 ft
60 ft
61 ft
59 ft
Question 14
Find the area of the triangle. If necessary, round the answer to two decimal places.
a = 12, b = 15, C = 52°
Question 14 options:
88.80
35.46
70.92
141.84
Question 15
Find the area of the triangle. If necessary, round the answer to two decimal places.
a = 19, b = 12, c = 14
Question 15 options:
92.84
83.84
89.84
86.84
Question 16
An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion. Develop a model that relates the distance d of the object from its rest position after t seconds.
m = 30, a = 6, b = 0.75, T = 6
Question 16 options:
d = -6e-0.75t/60 cos
d = -6e-0.75t/60 cos
d = 6e0.75t/60 cos
d = 6e-0.75t/60 cos
Question 17
Test the equation for symmetry with respect to the given axis, line, or pole.
r = 6 + 2 cos θ; the pole
Question 17 options:
May or may not be symmetric with respect to the pole
Symmetric with respect to the pole
Question 18
Find all the complex roots. Leave your answers in polar form with the argument in degrees.
The complex fifth roots of + i
Question 18 options:
(cos 30° + i sin 30°), (cos 102° + i sin 102°), (cos 174° + i sin 174°), (cos 246° + i sin 246°),
32(cos 30° + i sin 30°), 32(cos 102° + i sin 102°), 32(cos 174° + i sin 174°), 32(cos 246° + i sin 246°),
(cos 6° + i sin 6°), (cos 78° + i sin 78°), (cos 150° + i sin 150°), (cos 222° + i sin 222°),
32(cos 6° + i sin 6°), 32(cos 78° + i sin 78°), 32(cos 150° + i sin 150°), 32(cos 222° + i sin 222°),
Question 19
Use the figure below. Determine whether the given statement is true or false.
A + B + C + D + E = 0
Question 19 options:
True
False
Question 20
The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.
P = (1, 2); Q = (-2, -4)
Question 20 options:
v = 6i + 3j
v = -6i - 3j
v = 3i + 6j
v = -3i - 6j
Question 21
If v = -4i + 4j, find .
Question 21 options:
32
4
8
2
Question 22
Find the unit vector having the same direction as v.
v = -3i - 4j
Question 22 options:
u = - i - j
u = -15i - 20j
u = - i - j
u = i + j
Question 23
Find the direction angle of the vector v. Round to the nearest tenth if necessary.
v = -i + j
Question 23 options:
120°
135°
300°
150°
Question 24
A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 115 pounds, how much tension is in each part of the rope? Round your answers to the nearest tenth.
Question 24 options:
tension in the left part: -4893.0 lb;
tension in the right part: 4821.8 lb
tension in the left part: 400.3 lb;
tension in the right part: 460.2 lb
tension in the left part: -102.7 lb;
tension in the right part: -118.1 lb
tension in the left part: -93.5 lb;
tension in the right part: 92.2 lb
Question 25
Round your answer to the nearest tenth.
Find the work done by a force of 4 pounds acting in the direction of 44° to the horizontal in moving an object 4 feet from (0, 0) to (4, 0).
Question 25 options:
11.1 ft-lb
23.0 ft-lb
11.5 ft-lb
12.4 ft-lb
