Penn Foster Trigonometry exam

exam_007694rr_-_right_triangle_trigonometry exam_007696rr_-_graphs_of_trig_functions exam_007697rr_-_trigonometry_functions

Exam: 007694RR – RIGHT TRIANGLE

When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you
hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.

Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. Solar panels are used to convert energy from the sun into electricity. To get the best result, the panel has
to be perpendicular to the sun’s rays; in other words, angle θ has to be a right angle. What should the
height, h, be if θ is a right angle, a solar panel is 12 ft long, and the sun’s angle of elevation is 38°?

A. 9.4 ft

B. 15.4 ft

C. 7.4 ft

D. 9.5 ft

2. In a right triangle with g the right angle, a = 69.2° and c = 28.3. What is b?
A. 19.2

B. 26.5

C. 20.8

D. 10.0

3. A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along
the sides. How long should the diagonal be?
A. 11 ft

B. 10 ft

C. 14 ft

D. 12 ft

4. A stairway must be built to a deck that is 20 feet above ground level. To the nearest half foot, how far
from the base of the deck, on ground level, should the beginning of the stairway be placed so that the
stairway forms a 60° angle from the ground?
A. 12 ft

B. 35 ft

C. 11.5 ft

D. 11 ft

5. When viewing Angel Falls (the world’s highest waterfall) from Observation Platform A, located on the
same level as the bottom of the waterfall, we calculate the angle of elevation to the top of the waterfall to
be 69.30°. From Observation Platform B, which is located on the same level exactly 1000 feet from the
first observation point, we calculate the angle of elevation to the top of the waterfall to be 52.90°. How
high is the waterfall?
A. 2,646 ft

B. 1,322 ft

C. 998.5 ft

D. 2,643 ft

6. How many degrees does Earth turn during an eight-hour school day? (Assume that Earth makes one
revolution every 24 hours.)
A. 8°

B. 3°

C. 120°

D. 90°

7. A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of
the wheel after the wheel has completed one revolution?
A. 13.1 ft

B. 4.07 ft

C. 9.07 ft

D. 8.13 ft

8. In the triangle with g = 90°, β = 57.4°, and a = 70.0, which of the following measures is not correct?
(Hint: Solve the triangle.)
A. b = 109

B. c = 130

C. a = 32.6°
D. c = 134

9. What is sin θ?

A. 0.571

B. 0.575

C. 0.496

D. 0.495

10. Find the numerical measure of the largest angle of a triangle whose angle measures are 6x – 10°, 3x +
30°, and 2(45° – x).
A. 60°

B. 70°

C. 10°

D. 50°

11. A 16-foot ladder on ground level is leaning against a house. If the base of the ladder is placed 5.0 feet
from the house, what is the angle formed at the top of the ladder?
A. 18°

B. 72°

C. 24°

D. 20°

12.

A. x = 15

B. x = 10

C. x = 16

D. x = 12

13. In a right triangle with g the right angle, b = 86.5 and c = 125.8. What is β ?
A. 43.4°

B. 46.4°

C. 46.6°

D. 43.2°

14. Which of the following pairs of angles are coterminal?
A. 100° and 620°

B. 25° and –25°

C. 30° and 60°

D. 390° and 750°

15. A surveyor must divert her path from point C by proceeding due south for 300 ft to point A. The
surveyor determines that point B, which is due east of point C, is N49°E from point A. What is the distance
from point C to point B?
A. 375 ft

B. 370 ft

C. 350 ft

D. 360 ft

16. Find the height of the Barrington Space Needle if the angle measured from the ground 1000 ft
(measured to the nearest foot) from the point on the ground directly below the top of the needle is 58.15°.
A. 621.2 ft

B. 1,610 ft

C. 1,895 ft

D. 527.7 ft

17. Find the approximate value of x for the pieces of the truss shown in this figure.

A. 15 ft, 11 in.

B. 14 ft, 2 in.

C. 16 ft, 3 in.

D. 15 ft, 7 in.

18. Which angle measure is consistent with all of the following criteria?

(i) The reference angle is 40°.

(ii) The angle is more than one revolution.

(iii) The angle’s terminal side is in Quadrant II.

(iv) The angle isn’t positive.
A. –220°

B. 500°

C. –500°

D. –580°

19. A 6.00-foot person is casting a shadow of 4.20 feet. What time of the morning is it if the sun rose at
6:15 AM and will be directly overhead at 12:15 PM?
A. 9:55 AM

B. 8:35 AM

C. 8:58 AM

D. 9:40 AM

20. Convert 21°50″ to decimal degrees. Round your answer to the nearest thousandth.
A. 21.833°

B. 21.014°

End of exam

C. 21.0138°

D. 21.8333°

Exam: 007696RR – GRAPHS OF TRIG FUNCTIONS

1. A water wave has the equation y = 7.0 sin [0.65(x − 35.45t)], where x and y are measured in feet and t
is measured in seconds. In miles per hour, what is the phase velocity (speed) of the wave?
A. 35.45 mph

B. 24.17 mph

C. 9.67 mph

D. 14.0 mph

3. Which of these standard trigonometric functions has the least period?
A. cosine

B. cosecant

C. tangent

D. secant

A. None

B. 1

C. 3

D. Infinitely many

5. Which of these functions has period 7?

C.
D.

B. 6p

7. Which standard trigonometric function is graphed below?

A. Cotangent

B. Secant

C. Tangent

D. Cosecant

8. Which of these statements are true??

(i) The domain of the inverse cosine function (y = cos–1 x) is –1 ≤ x ≤ 1.

(ii) The range of the inverse sine function (y = sin–1 x) is 0 ≤ y ≤ p .

(iii) The range of the inverse tangent function (y = tan–1 x) is –p/2 < y < p/2.

A. (i) and (iii)

B. (i), (ii), and (iii)

C. (ii) and (iii)

D. (i) and (ii)

9. Choose the graph of y = sec x.
A.

B.
C.
D.

10. What is the period of the graph?

A. 3.5

B. 3

C. 1.5

D. 7

11. What is the amplitude of this graph?

A. 1.5

B. 2

C. 2.5

D. 5

12.

A. 7

B. 4

C. 10

D. 6

13. Which of the following lists contains only functions with vertical asymptotes in their graphs?
A. Cosine, sine, secant, cosecant

B. Sine, tangent, secant, cosecant

C. Tangent, secant, cosecant, cotangent

D. Cosine, sine, tangent, cotangent

14.

A. 3

B.
C.
D.

15. What is the equation for shifting the standard sine curve +2 units horizontally?
A. y = sin x − 2
B. y = sin (x − 2)

C. y = sin x + 2

D. y = sin (x + 2)

16. What is the translation point of y = 100 tan (6x) + 4?
A. (6, 4)

B. (6, −4)
C. (0, 4)

D. (0, −4)

17. What is the equation of a cosine function with amplitude 3, transition point (−1, 1), and period p ?
A. y = 3 cos [2(x − 1)] + 1
B. y = p cos [3(x − 1)] − 1
C. y = 3 cos [2(x + 1)] + 1

D. y = 3 cos [p (x + 1)] − 1

18. Choose the equation that most likely matches the graph below.

A. y = cot–1 x

B. y = tan–1 x

C. y = sec–1 x

D. y = csc–1 x

19. cot–1 −0.57735 is approximately
A. −0.65.
B. 2.09.

C. 2.62.

D. −1.05.

20.

A.
B.

End of exam

C.
D.

1. Find the complete exact solution of sin x = .

2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to
two decimal places.

3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two
decimal places.

−
3

E
x
a
m
in
a
t
io
n

Trigonometric Functions

Clearly number your answers and save them in a Word file.
Upload your file as instructed in the Lesson 2 Review.

Go to http://www.takeexamsonline.com to submit your answers
online. Click on Take Exam next to Lesson 4. Then click on
Submit Files.

Questions 1–20: Answer the following questions.

EXAMINATION NUMBER

00769700

Examination2

4. Prove that tan2 � – 1 + cos2 � = tan2 � sin2 �.

5. Prove that tan � sin � + cos � = sec �.

6. Prove that = cos � + sin �.

7. Prove that .

8. Prove that = cos � – cot � cos �.

9. Find a counterexample to shows that the equation sec � – cos � = sin � sec � is not
an identity.

sin cos

tan sin cos tan

2 2ω ω
ω ω ω ω

−
+

1 + tan

1 tan

sec + 2tan

1 tan
2
2

θ
θ

θ θ
θ− −

tan cos +

sin

2 2λ λ λ
λ

Examination 3

10. Write tan as a function of � only.

11. Write cos as a function of � only.

12. Write cos(–83°) as a function of a positive angle.

. Write sin(125°) in terms of its cofunction. Make sure your answer is a function
of a positive angle.

14. Find the exact value of sin(195°).

15. Sketch a graph of y = sin(–2x), paying particular attention to the critical points.

λ
π

+
3

⎛
⎝
⎜⎜⎜

⎞
⎠
⎟⎟⎟⎟

π
β

−

⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
2
4

–4

–2
π 2π

Examination4

16. If cot 2� = with 0 � 2� � �, find cos�, sin�, and tan�.

17. Find the exact value of sin2� if cos� = (� in Quadrant I).

18. Find the exact value of tan2� if sin� = (� in Quadrant II).

19. Solve sin 2x + sin x = 0 for 0 � x � 2�.

20. Write 2sin37°sin26° as a sum (or difference).

4
5
5
13

Turn in your highest-quality paper
Get a qualified writer to help you with

“ Penn Foster Trigonometry exam ”

Get high-quality paper

NEW! AI matching with writer

Still stressed with your coursework?

Get quality coursework help from an expert!

Order now