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MAC 1114 Module Test 7
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the following as an algebraic expression in u, u > 0.
1) sin arcsin u
3
A)
u2 + 3
u2 + 3
B) u
3
C) u
3
3
D) u
u2 - 3
u2 - 3
Answer: B
Objective: (6.1) Write Function Value in Terms of u
Using a calculator, evaluate the expression.
2) sec (arctan 4.839)
A) 4.9412
B) .2024
C) .4999
D) 1.0000
C) 2.74126980
D) 2.82857139
Answer: A
Objective: (6.1) Evaluate Inverse Expression (Approximate)
Use a calculator to give the real number value.
3) y = cos-1(-.9397)
A) 2.79254838
B) -.34920634
Answer: A
Objective: (6.1) Find Approximate Value of Inverse Function (Real Number)
Find the exact value of the real number y.
4) y = arctan
3
3
A) π
3
B) π
6
C) 5π
6
D) 1π
4
Answer: B
Objective: (6.1) Find Exact Value of Inverse Function (Real Number)
Use a calculator to give the value in decimal degrees.
5) sec-1 7.246
A) θ = -7.86°
B) θ = 7.86°
C) θ = 7.93°
D) θ = 82.07°
Answer: D
Objective: (6.1) Find Inverse (Approximate, Degrees)
Write the following as an algebraic expression in u, u > 0.
6) sin(arctan u)
A) u
u2 - 1
u2 - 1
B)
u2 + 1
u2 + 1
C) u
Answer: D
Objective: (6.1) Write Function Value in Terms of u
1
u2 + 1
D) u
u2 + 1
u2 + 1
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
Provide an appropriate response.
7) True or False? To calculate inverse secant on a calculator use the fact that sec-1 x =
Answer:
True
1
.
cos-1 x
False
Objective: (6.1) *Know Concepts: Inverse Circular Functions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
8) The range r of a projectile is given by
r = 1 v 2 sin 2θ,
32
where v is the initial velocity and θ is the angle of elevation. If r is to be 2000 ft and v = 4500 ft/sec, what
must the angle of elevation be? Give your answer in degrees to the nearest hundredth.
A) 0.18°
B) 89.91°
C) 0.09°
D) 0.13°
Answer: C
Objective: (6.2) Solve Apps: Trigonometric Equations I
Solve the equation exactly over the interval [0, 2π).
9) 2 sin 2x = sin x
A)
π , 2π
3 3
B) 0, π, π , 5π
6 6
C)
π , 3π , π , 2π
2 2 3 3
D)
π , 5π
6 6
C)
3π , 5π
4
4
Answer: B
Objective: (6.2) Find All Angles in [0, 2pi) That Satisfy Eqn (Exact)
10) cos x = sin x
A) π , 7π
4 4
B)
3π , 7π
4
2
Answer: D
Objective: (6.2) Find All Angles in [0, 2pi) That Satisfy Eqn (Exact)
Solve the equation exactly over the interval [0,360°).
11) (tan θ + 1)(2 cos θ - 1) = 0
A) {0°, 135°, 225°}
C) {45°, 60°, 225°, 240°}
B) {30°, 135°, 150°, 315°}
D) {60°, 135°, 300°, 315°}
Answer: D
Objective: (6.2) Solve Trigonometric Equation of [0, 360)
2
D)
π , 5π
4 4
Solve the equation exactly over the interval [0, 2π).
12) sin x + 4 = 3
A) π , 2π
B) 3π
3 3
2
C) {0, π}
D)
π
2
Answer: B
Objective: (6.2) Find All Angles in [0, 2pi) That Satisfy Eqn (Exact)
Solve the problem.
13) 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 = 30 ft, d = 80 ft, and B = 56°. Give your answer in degrees to the nearest hundredth.
A) 21.76°
B) 16.66°
C) 26.51°
D) 11.28°
Answer: B
Objective: (6.2) Solve Apps: Trigonometric Equations I
Solve the equation exactly over the interval [0, 2π).
14) tan 2x - tan x = 0
A) π , 5π
4 4
B)
C) {0, π}
π , π , 2π , 7π , 7π , 13π , 5π
12 6 3 12 6
12
3
D) {0}
Answer: C
Objective: (6.3) Solve Trigonometric Equation of [0, 2pi)
Solve.
15) The weekly sales in thousands of items of a product has a seasonal sales record approximated by
n = 66.83 + 26 sin πt
24
(t = time in weeks with t=1 referring to the first week in the year). During which week(s) will the sales equal
79,830 items?
A) week 21 and week 30
B) week 4 and week 47
C) week 4, week 20, and week 52
D) week 30 and week 47
Answer: C
Objective: (6.3) Solve Apps: Trigonometric Equations II
Solve the equation exactly over the interval [0, 2π).
16) 2 3 sin 4x = 3
A) π , π , 2π , 7π , 7π , 13π , 5π , 19π
12 6 3 12 6
12
3
12
C)
B) {0}
π , 5π
4 4
D) 0, π , π
4
Answer: A
Objective: (6.3) Solve Trigonometric Equation of [0, 2pi)
3
Solve.
17) In an electrical circuit, let V represent the electromagnetic force in volts at t seconds. Assume V = cos 2πt.
Find the smallest positive value of t where 0 ≤ t ≤ 1 for V =
2
A) 1 sec
12
B) 1 sec
2
2
3.
C) 1 sec
6
Answer: A
Objective: (6.3) Solve Apps: Trigonometric Equations II
Solve the equation exactly over the interval [0, 2π).
18) cos 2x = 2 - cos 2x
A) 0, 2π , π, 4π
3
3
C)
B) ∅
π , 3π , 5π , 7π
4 4
4
4
D)
π , 9π , 7π , 15π
8 8
8
8
Answer: D
Objective: (6.3) Solve Trigonometric Equation of [0, 2pi)
Solve the equation exactly over the interval [0,360°).
19) sin 2θ = cos θ
A) {30°, 90°, 150°, 270°}
C) {105°, 165°, 285°, 345°}
B) {0°, 120°, 180°, 240°}
D) {15°, 165°, 195°, 345°}
Answer: A
Objective: (6.3) Solve Trigonometric Equation of [0, 360)
Solve the equation exactly over the interval [0, 2π).
20) sin 2x + sin x = 0
B) , 2π , π, 4π
3
3
A) ∅
C)
π , 3π , 5π , 7π
4 4
4
4
D)
Answer: B
Objective: (6.3) Solve Trigonometric Equation of [0, 2pi)
4
π , 9π
8 8
D) 0 sec