Course Name: Second Year Algebra 2
Student: Aguistin Spaan
Course ID: MTHH040059
ID: G87557040
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.
____ 2.
Find the exact value of cos 480°. Use a double-angle identity.
a.
b.
1
c.
d.
0
−1
Identify the amplitude and period of this function: y =
a.
b.
____ 3.
tan (2
n is an integer,
,2
c.
none because no maximum or minimum value exist;
d.
none because no maximum or minimum value exist;
Find the measure of x to the nearest tenth.
a.
b.
c.
d.
____ 4.
−
36.5°
52.4°
91.1°
79.3°
Solve this equation for 0 ≤ θ ≤
a.
b.
c.
d.
:
sin θ –
= 0.
)x.
____ 5.
Find the exact sine value of −30°
a.
b.
c.
d.
____ 6.
−
Find the maximum value of this function:
a.
b.
c.
d.
____ 7.
−
6
0
5
8
Find the exact value of cos 22.5° . Use a half-angle identity.
a.
b.
c.
d.
____ 8.
____ 9.
−
Identify the amplitude and period of this function: y = 3 cos θ.
a.
2, 3
b.
6, 2
c.
3,
d.
3, 2
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
radians.
____ 10. Find the measure of x to the nearest tenth.
a.
b.
c.
d.
43.0°
25.6°
39.8°
75.2°
____ 11. Find the exact cosine value of 390°.
a.
b.
c.
−
d.
−1
____ 12. Identify the amplitude and period of this function: y = 4 sin 3θ.
a.
2,
b.
2,
c.
4,
d.
4,
____ 13. Verify this identity: tan θ cot θ = 1.
a.
cos θ •
b.
•
c.
sin θ •
d.
0=0
____ 14.
=1
=1
=1
is a right triangle, with
a.
b.
c.
d.
5.4
5.7
6.3
8.6
being the right angle. m
= 51°, b = 8, find a.
____ 15.
is a right triangle with m
= 90°. RS = 48, cos R =
; Find cot R.
a.
b.
c.
d.
____ 16. Find the exact value of tan 330°. Use the sum or difference identity.
a.
b.
c.
d.
−
____ 17. Find the period of this function:
a.
b.
c.
d.
2
4
6
8
____ 18. Find the value in radians of sin–1(–1.0).
a.
b.
c.
d.
no solution
−0.4794
−1.5708
−0.0500
____ 19. Use either the Law of Sines or the Law of Cosines. In
a.
b.
c.
d.
111.7°
56.3°
89.8°
24.5°
, d = 6 in., e = 7 in., and f = 12 in. Find m
.
____ 20. In a circle, an arc of length 25.1 in. is intercepted by a central angle of
circle? Round to the nearest whole number.
a.
b.
c.
d.
33 in.
19 in.
11 in.
6 in.
____ 21. Simplify this expression:
a.
b.
c.
d.
sin2 θ
0
1
.
radians. What is the radius of the
____ 22. Identify the graph of this function from 0 to 2 : y = 4 cos x.
a.
b.
c.
d.
____ 23. Find the measure of an angle between 0° and 360° degrees coterminal with 385 degrees.
a.
b.
c.
d.
−155°
25°
155°
−25°
____ 24. Use either the Law of Sines or the Law of Cosines. In
Find RS.
a.
b.
c.
d.
6.6 in.
10.4 in.
12.2 in.
29.5 in.
,m
= 35°, m
= 48°, and TS = 8 in.
____ 25. Identify the amplitude and period of this function: y = 4 cos
a.
4, 6
b.
3, 6
c.
3, 4
d.
4, 3
____ 26. Use either the Law of Sines or the Law of Cosines. In
.
a.
b.
c.
d.
38.3°
19.6°
7.5°
26.7°
____ 27. Write this measure in radians: –60°.
a.
−
b.
−
c.
d.
____ 28. Write this measure in degrees: −3
a.
b.
c.
d.
radians.
−1080°
−60°
−180°
−540°
____ 29. Find the minimum value of this function:
a.
b.
c.
d.
−4
4
2
−2
.
,m
= 21°, d = 6 in., and f = 16 in. Find m
____ 30.
is a right triangle with m
= 90°. RS = 30, cos R =
; Find sin R.
a.
b.
c.
d.
____ 31. 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
____ 32. Solve this equation for 0 ≤ θ < 2
a.
0,
b.
,
c.
, −1
d.
: sin θ cos θ – cos θ = 0.
−1,
____ 33. Write this measure in radians: 100°.
a.
100
b.
c.
d.
____ 34. Simplify this expression: sec θ cos θ sin θ.
a.
b.
c.
d.
sin2 θ
sin θ
1
____ 35. Identify the domain and range of this function: y = 2 cos
a.
d: all real numbers; r:−
b.
c.
d: −2 ≤ x ≤ 2; r: all real numbers
d.
d: all real numbers; r: −2 ≤ y ≤ 2
d: −
≤x≤
≤y≤
; r: all real numbers
____ 36. Write this measure in degrees: 6
a.
b.
c.
d.
θ.
radians.
2160°
30°
1080°
180°
____ 37. How many cycles does the sine function, y = sin 5θ, have in the interval from 0 to 2
a.
b.
c.
d.
?
2
3
4
5
____ 38. Use the graph above to find the value of y = sin θ for the value 30°.
a.
b.
c.
d.
−1
0.5
0
1
____ 39. Use either the Law of Sines or the Law of Cosines. In
a.
b.
c.
d.
16.3 in.
14.2 in.
21.8 in.
24.2 in.
____ 40. 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
,m
= 65°, d = 19 in., and f = 25 in. Find e.
____ 41. Find the measure of the angle in standard position.
a.
b.
c.
d.
135°
−225°
−135°
225°
____ 42. Write this measure in radians: 450°.
a.
b.
450
c.
d.
____ 43. Find the exact value of cos 15°. Use the sum or difference identity.
a.
b.
c.
d.
____ 44. How many cycles does the sine function have in the interval 0 to 2
a.
b.
c.
d.
1
2
3
____ 45. Write this measure in degrees:
a.
b.
c.
d.
180°
150°
300°
15°
radians.
?
____ 46. Describe the phase shift and determine the value of “h” in the translation; y = sin (x + 1).
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 =
____ 47. The period of a periodic function is 10 s. How many cycles does it go through in 45 s?
a.
cycle
b.
c.
d.
4.5 cycles
450 cycles
2 cycles
____ 48. Evaluate this expression in radians: csc
.
a.
b.
c.
d.
2
____ 49. Use the graph above to find the value of y = sin θ for the value
a.
b.
c.
d.
radians.
0.5
0
1
−1
____ 50. 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.
100 ft, 200 ft
140 ft, 229 ft
150 ft, 215 ft
125 ft, 225 ft
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.
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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
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Tables
MTHH 040
blank page
Tables
MTHH 040