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This is the Progress 3 Test for Algebra 2. The test has tables attached to the bottom to help out with most of the questions. I believe you might need a calculator, and if anything else is needed, please let me know. I need all the questions answered correctly. Thank you 🙂
Course Name: Second Year Algebra 2
Student: Ryan Neutel
Course ID: MTHH040059
ID: C98848142
Submittal: 59
Progress Test 3
Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is
important that you do your own work. Select the response that best completes the statement or answers the question.
Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions.
____ 1.
Find the value in radians of tan–1 (–1.2).
a.
b.
c.
d.
____ 2.
Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of
elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building
is 35°. How tall is each building?
a.
b.
c.
d.
____ 3.
−1.1415
−0.8761
−2.5722
no solution
100 ft, 200 ft
140 ft, 229 ft
150 ft, 215 ft
125 ft, 225 ft
Simplify this expression: sin θ csc θ.
a.
b.
c.
d.
____ 4.
sin2 θ
0
1
Solve this equation for 0 ≤ θ < 2
a.
b.
0, 1
, −1
c.
0,
d.
0,
____ 5.
,2
is a right triangle with m
a.
b.
c.
d.
: sin θ cos θ + sin θ = 0.
= 90°. RS = 48, cos R =
; Find cot R.
____ 6.
Use either the Law of Sines or the Law of Cosines. In
Find RS.
a.
b.
c.
d.
____ 7.
,m
= 78°, m
6.6 in.
10.4 in.
12.2 in.
29.5 in.
Write this measure in radians: 80°.
a.
80
b.
c.
d.
____ 8.
Find the exact sine value of −30°
a.
b.
c.
d.
____ 9.
−
−
Name two different times when the hands of a clock show an angle of
a.
b.
c.
d.
1:00, 11:00
2:00, 10:00
3:00, 9:00
4:00, 8:00
____ 10. Evaluate this expression in radians: csc
a.
b.
c.
d.
2
.
radians.
= 39°, and TS = 19 in.
____ 11. Identify the amplitude and period of this function: y = 3 sin 5θ.
a.
5,
b.
3,
c.
3,
d.
5,
____ 12.
is a right triangle with m
= 90°. RS = 30, cos R =
; Find sin R.
a.
b.
c.
d.
____ 13. Write this measure in degrees:
a.
b.
c.
d.
radians.
288°
225°
144°
180°
____ 14. Use the graph above to find the value of y = sin θ for the value 150°.
a.
b.
c.
d.
−1
−0.5
0.5
1
____ 15. Find the measure of x to the nearest tenth.
a.
b.
c.
d.
29.5°
38.5°
112.4°
54.4°
____ 16. Identify the amplitude and period of this function: y = 3 cos
a.
3, 3
b.
3, 10
c.
5, 10
d.
5, 3
____ 17. Use either the Law of Sines or the Law of Cosines. In
.
a.
b.
c.
d.
111.8°
56.3°
89.8°
24.5°
____ 18. Find the measure of the angle in standard position.
a.
b.
c.
d.
−340°
−380°
−20°
340°
____ 19. Find the exact value of sin 15° . Use a half-angle identity.
a.
b.
c.
d.
.
, d = 10 in., e = 20 in., and f = 14 in. Find m
____ 20. Use either the Law of Sines or the Law of Cosines. In
a.
b.
c.
d.
,m
= 65°, d = 19 in., and f = 25 in. Find e.
16.3 in.
14.2 in.
21.8 in.
24.2 in.
____ 21. Verify this identity: tan θ cot θ = 1.
a.
cos θ •
b.
=1
•
c.
sin θ •
d.
0=0
=1
=1
____ 22. Describe the phase shift and determine the value of “h” in the translation; y = sin (x +
a.
units to the left; h = −
b.
c.
1 unit to the left; h = −1
units to the right; h =
d.
1 unit to the right; h =
____ 23. Identify the amplitude and period of this function: y =
a.
b.
c.
d.
tan
).
x.
none because no maximum or minimum value exist; 1
n is an integer;
;
none because no maximum or minimum value exist;
____ 24. Find the measure of an angle between 0° and 360° degrees coterminal with 575 degrees.
a.
b.
c.
d.
215°
−145°
35°
145°
____ 25. Describe the translation in y = cos (x + 1) – 2.
a.
b.
c.
d.
left 1 unit; down 2 units
left 1 unit; up 2 units
right 1 unit; down 2 units
right 1 unit; up 2 units
____ 26. Identify the domain and range of this function: y = 3 cos θ.
a.
b.
c.
d.
d: −3 ≤ x ≤ 3; r: all real numbers
d: all real numbers; r: −3 ≤ y ≤ 3
d: all real numbers; r: −1 ≤ y ≤ 1
d: −1 ≤ x ≤ 1; r: all real numbers
____ 27. The period of a periodic function is 2.5 s. How many cycles does it go through in 20 s?
a.
b.
c.
d.
cycle
2 cycles
50 cycles
8 cycles
____ 28. Write this measure in radians: –60°.
a.
−
b.
−
c.
d.
____ 29. In a circle, an arc of length 43.2 cm is intercepted by a central angle of
the circle? Round to the nearest whole number.
a.
b.
c.
d.
54 cm
17 cm
11 cm
35 cm
____ 30. How many cycles does the sine function have in the interval 0 to 2 ?
a.
b.
c.
d.
1
2
3
____ 31. Find the period of this function:
a.
b.
c.
d.
2
4
6
8
radians. What is the radius of
____ 32. How many cycles does the sine function, y = 3 sin θ, have in the interval from 0 to 2
a.
b.
c.
d.
1
2
3
4
____ 33. Find the exact value of cos 720°. Use a double-angle identity.
a.
b.
c.
d.
1
−1
0
−
____ 34. Find the measure of x to the nearest tenth.
a.
b.
c.
d.
21.6°
15.9°
33.7°
46.1°
____ 35. Find the exact value of tan 300°. Use the sum or difference identity.
a.
b.
c.
d.
−
____ 36. Identify the amplitude and period of this function: y = 3 cos θ.
a.
2, 3
b.
6, 2
c.
3,
d.
3, 2
?
____ 37. Find the maximum value of this function:
a.
b.
c.
d.
4
3
−3
−4
____ 38. Identify the graph of this function from 0 to 2 : y = 4 cos x.
a.
b.
c.
d.
____ 39. Solve this equation for 0 ≤ θ ≤
:
sin θ –
= 0.
a.
b.
c.
d.
____ 40. Use the graph above to find the value of y = sin θ for the value
a.
b.
c.
d.
radians.
0
0.5
1
−1
____ 41. A triangle with side lengths 6 in and 8 in and the measure of the angle between them is 51 degrees. What is
the area of the triangle?
a.
61.3 in.2
b.
81.9 in.2
c.
42.6 in.2
d.
18.7 in.2
____ 42. Write this measure in radians: 450°.
a.
b.
450
c.
d.
____ 43. Use either the Law of Sines or the Law of Cosines. In
.
a.
b.
c.
d.
38.3°
19.6°
7.5°
26.7°
,m
= 21°, d = 6 in., and f = 16 in. Find m
____ 44. Find the minimum value of this function:
a.
b.
c.
d.
4
3
−3
−4
____ 45. Find the exact cosine value of −30°.
a.
b.
c.
d.
−
−
____ 46. Write this measure in degrees: −4
a.
b.
c.
d.
radians.
−720°
−1440°
−45°
−180°
____ 47. Find the exact value of cos 75°. Use the sum or difference identity.
a.
b.
c.
d.
____ 48.
is a right triangle, with
a.
b.
c.
d.
19.8
2.4
5.6
12.2
being the right angle. m
= 68°, b = 8, find a.
____ 49. Write this measure in degrees: 6
a.
b.
c.
d.
radians.
2160°
30°
1080°
180°
____ 50. Simplify this expression:
.
a.
b.
c.
d.
sin2 θ
0
1
Carefully review your answers on this progress test and make any corrections you feel are necessary. When
you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the
online test submission page in the presence of your proctor.
The University of Nebraska is an equal opportunity educator and employer. ©2019, The Board of Regents of the
University of Nebraska. All rights reserved.
Second Year Algebra 2: Trigonometry
Summary of Formulas
Summary of Tables
MTHH 040
TABLES
Included in this section are two sets of tables. The first is the Table of Trigonometric Functions for
angles written in degrees and the second is the Table of Trigonometric Functions for angles written
in radians.
Summary of Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
blank page
Tables
MTHH 040
Course Name: Second Year Algebra 2
Student: Ryan Neutel
Course ID: MTHH040059
ID: C98848142
Submittal: 59
Progress Test 3
Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is
important that you do your own work. Select the response that best completes the statement or answers the question.
Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions.
____ 1.
Find the value in radians of tan–1 (–1.2).
a.
b.
c.
d.
____ 2.
Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of
elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building
is 35°. How tall is each building?
a.
b.
c.
d.
____ 3.
−1.1415
−0.8761
−2.5722
no solution
100 ft, 200 ft
140 ft, 229 ft
150 ft, 215 ft
125 ft, 225 ft
Simplify this expression: sin θ csc θ.
a.
b.
c.
d.
____ 4.
sin2 θ
0
1
Solve this equation for 0 ≤ θ < 2
a.
b.
0, 1
, −1
c.
0,
d.
0,
____ 5.
,2
is a right triangle with m
a.
b.
c.
d.
: sin θ cos θ + sin θ = 0.
= 90°. RS = 48, cos R =
; Find cot R.
____ 6.
Use either the Law of Sines or the Law of Cosines. In
Find RS.
a.
b.
c.
d.
____ 7.
,m
= 78°, m
6.6 in.
10.4 in.
12.2 in.
29.5 in.
Write this measure in radians: 80°.
a.
80
b.
c.
d.
____ 8.
Find the exact sine value of −30°
a.
b.
c.
d.
____ 9.
−
−
Name two different times when the hands of a clock show an angle of
a.
b.
c.
d.
1:00, 11:00
2:00, 10:00
3:00, 9:00
4:00, 8:00
____ 10. Evaluate this expression in radians: csc
a.
b.
c.
d.
2
.
radians.
= 39°, and TS = 19 in.
____ 11. Identify the amplitude and period of this function: y = 3 sin 5θ.
a.
5,
b.
3,
c.
3,
d.
5,
____ 12.
is a right triangle with m
= 90°. RS = 30, cos R =
; Find sin R.
a.
b.
c.
d.
____ 13. Write this measure in degrees:
a.
b.
c.
d.
radians.
288°
225°
144°
180°
____ 14. Use the graph above to find the value of y = sin θ for the value 150°.
a.
b.
c.
d.
−1
−0.5
0.5
1
____ 15. Find the measure of x to the nearest tenth.
a.
b.
c.
d.
29.5°
38.5°
112.4°
54.4°
____ 16. Identify the amplitude and period of this function: y = 3 cos
a.
3, 3
b.
3, 10
c.
5, 10
d.
5, 3
____ 17. Use either the Law of Sines or the Law of Cosines. In
.
a.
b.
c.
d.
111.8°
56.3°
89.8°
24.5°
____ 18. Find the measure of the angle in standard position.
a.
b.
c.
d.
−340°
−380°
−20°
340°
____ 19. Find the exact value of sin 15° . Use a half-angle identity.
a.
b.
c.
d.
.
, d = 10 in., e = 20 in., and f = 14 in. Find m
____ 20. Use either the Law of Sines or the Law of Cosines. In
a.
b.
c.
d.
,m
= 65°, d = 19 in., and f = 25 in. Find e.
16.3 in.
14.2 in.
21.8 in.
24.2 in.
____ 21. Verify this identity: tan θ cot θ = 1.
a.
cos θ •
b.
=1
•
c.
sin θ •
d.
0=0
=1
=1
____ 22. Describe the phase shift and determine the value of “h” in the translation; y = sin (x +
a.
units to the left; h = −
b.
c.
1 unit to the left; h = −1
units to the right; h =
d.
1 unit to the right; h =
____ 23. Identify the amplitude and period of this function: y =
a.
b.
c.
d.
tan
).
x.
none because no maximum or minimum value exist; 1
n is an integer;
;
none because no maximum or minimum value exist;
____ 24. Find the measure of an angle between 0° and 360° degrees coterminal with 575 degrees.
a.
b.
c.
d.
215°
−145°
35°
145°
____ 25. Describe the translation in y = cos (x + 1) – 2.
a.
b.
c.
d.
left 1 unit; down 2 units
left 1 unit; up 2 units
right 1 unit; down 2 units
right 1 unit; up 2 units
____ 26. Identify the domain and range of this function: y = 3 cos θ.
a.
b.
c.
d.
d: −3 ≤ x ≤ 3; r: all real numbers
d: all real numbers; r: −3 ≤ y ≤ 3
d: all real numbers; r: −1 ≤ y ≤ 1
d: −1 ≤ x ≤ 1; r: all real numbers
____ 27. The period of a periodic function is 2.5 s. How many cycles does it go through in 20 s?
a.
b.
c.
d.
cycle
2 cycles
50 cycles
8 cycles
____ 28. Write this measure in radians: –60°.
a.
−
b.
−
c.
d.
____ 29. In a circle, an arc of length 43.2 cm is intercepted by a central angle of
the circle? Round to the nearest whole number.
a.
b.
c.
d.
54 cm
17 cm
11 cm
35 cm
____ 30. How many cycles does the sine function have in the interval 0 to 2 ?
a.
b.
c.
d.
1
2
3
____ 31. Find the period of this function:
a.
b.
c.
d.
2
4
6
8
radians. What is the radius of
____ 32. How many cycles does the sine function, y = 3 sin θ, have in the interval from 0 to 2
a.
b.
c.
d.
1
2
3
4
____ 33. Find the exact value of cos 720°. Use a double-angle identity.
a.
b.
c.
d.
1
−1
0
−
____ 34. Find the measure of x to the nearest tenth.
a.
b.
c.
d.
21.6°
15.9°
33.7°
46.1°
____ 35. Find the exact value of tan 300°. Use the sum or difference identity.
a.
b.
c.
d.
−
____ 36. Identify the amplitude and period of this function: y = 3 cos θ.
a.
2, 3
b.
6, 2
c.
3,
d.
3, 2
?
____ 37. Find the maximum value of this function:
a.
b.
c.
d.
4
3
−3
−4
____ 38. Identify the graph of this function from 0 to 2 : y = 4 cos x.
a.
b.
c.
d.
____ 39. Solve this equation for 0 ≤ θ ≤
:
sin θ –
= 0.
a.
b.
c.
d.
____ 40. Use the graph above to find the value of y = sin θ for the value
a.
b.
c.
d.
radians.
0
0.5
1
−1
____ 41. A triangle with side lengths 6 in and 8 in and the measure of the angle between them is 51 degrees. What is
the area of the triangle?
a.
61.3 in.2
b.
81.9 in.2
c.
42.6 in.2
d.
18.7 in.2
____ 42. Write this measure in radians: 450°.
a.
b.
450
c.
d.
____ 43. Use either the Law of Sines or the Law of Cosines. In
.
a.
b.
c.
d.
38.3°
19.6°
7.5°
26.7°
,m
= 21°, d = 6 in., and f = 16 in. Find m
____ 44. Find the minimum value of this function:
a.
b.
c.
d.
4
3
−3
−4
____ 45. Find the exact cosine value of −30°.
a.
b.
c.
d.
−
−
____ 46. Write this measure in degrees: −4
a.
b.
c.
d.
radians.
−720°
−1440°
−45°
−180°
____ 47. Find the exact value of cos 75°. Use the sum or difference identity.
a.
b.
c.
d.
____ 48.
is a right triangle, with
a.
b.
c.
d.
19.8
2.4
5.6
12.2
being the right angle. m
= 68°, b = 8, find a.
____ 49. Write this measure in degrees: 6
a.
b.
c.
d.
radians.
2160°
30°
1080°
180°
____ 50. Simplify this expression:
.
a.
b.
c.
d.
sin2 θ
0
1
Carefully review your answers on this progress test and make any corrections you feel are necessary. When
you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the
online test submission page in the presence of your proctor.
The University of Nebraska is an equal opportunity educator and employer. ©2019, The Board of Regents of the
University of Nebraska. All rights reserved.
Second Year Algebra 2: Trigonometry
Summary of Formulas
Summary of Tables
MTHH 040
TABLES
Included in this section are two sets of tables. The first is the Table of Trigonometric Functions for
angles written in degrees and the second is the Table of Trigonometric Functions for angles written
in radians.
Summary of Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
Tables
MTHH 040
blank page
Tables
MTHH 040
