Course Name: Precalculus: Trigonometry
Student: Kwinda Netshitangani
Course ID: MTHH044059
ID: J47865775
Submittal: 59
Progress Test 3
Progress Test 3 (Evaluation 59) covers the course materials that were assigned in Units 5 and 6. Although the progress
test is similar in style to the unit evaluations, the progress test is a closed-book test. You may not have access to
notes or any of the course materials while you are taking the test. You may also use your graphing calculator on
this test.
The Summary of Formulas and Trigonometric Tables from the Appendix is included for your use during the
test.
____ 1.
What is one of the three pairs of polar coordinates for the point (5, 210°) with –360° < Θ ≤ 360°?
a.
b.
c.
d.
____ 2.
Solve the triangle for the unknown parts.
a = 48, B = 50°, C = 62°, c = ____
a.
b.
c.
d.
____ 3.
____ 5.
109
46
50
24
The horizontal and vertical components of a vector are 20 feet and 15 feet respectively. Find the magnitudes
of the resultant vector and the angle that it forms with the horizontal. What is the magnitude?
a.
b.
c.
d.
____ 4.
(5, 150°)
(–5, 150°)
(–5, –150°)
(5, –150°)
40 feet
35 feet
25 feet
5 feet
Transform from polar coordinates to rectangular coordinates: (
a.
b.
(1, −1)
(
,
c.
d.
(1, 1)
(−1, −1)
)
Use logarithms to evaluate
a.
b.
c.
d.
.00342
.000342
.00104
.0104
. What is the answer?
, 45°)
____ 6.
The horizontal and vertical components of a vector are 8 inches and 2 inches respectively. What is the
angle that it forms with the horizontal?
a.
b.
c.
d.
____ 7.
Given that
a.
b.
c.
d.
____ 8.
= 5i − 12j, and
= 6i − 8j, find 2
−3 .
– 8 i – 48 j
3 i – 52 j
–8i
3 i – 20 j
Simplify the following: i10
a.
b.
c.
d.
____ 9.
14°
28°
7°
45°
1
−1
i
–i
Given that
a.
b.
c.
d.
= 3i + 4j, and
= 5i − 12j, find
·
.
56
63
–16
–33
____ 10. Solve for the unknown part of the triangle, if it exists. If c = 74, b = 48, and C = 74°, then what does B = ?
a.
b.
c.
d.
45°10’
17°50’
25°20’
38°30’
____ 11. Solve for the unknown part of the triangle, if it exists. If b = 60, a = 82, and A = 115°, then what does c = ?
a.
b.
c.
d.
41
36
72
12
____ 12. 9x = 27; x =
a.
b.
c.
d.
3
____ 13.
Express
as an algebraic sum of logarithms.
a.
log 6 +
b.
(log 6 + log 5 − log 51 − log 16)
c.
log 6 +
log 5 +
log 5 −
log 51 +
log 51 −
log 16
log 16
d.
____ 14. log5 x = 3; x =
a.
b.
c.
d.
243
125
625
729
____ 15. Given that
= 2i − 3j, and
= 5i + 7j, find a unit vector parallel to
.
a.
b.
c.
d.
____ 16. log
a.
b.
c.
4 = x; x =
–2
2
d.
____ 17. A vector 20 inches in length forms angles of 58° and 22° with two component vectors. Find the magnitudes
of the two vectors. The magnitude of one vector = ?
a.
b.
c.
d.
17.2 inches
23.2 inches
12.5 inches
18.5 inches
____ 18. Perform the indicated operation, leave the answers in the rectangular form a + bi.
Simplify: 7i2 + 8i3 + 9i4 + 10i5.
a.
b.
c.
d.
16 + 2 i
2+2i
16 + 18 i
2 + 18 i
____ 19. Given a = 27, b = 36, c = 49. What is the area of triangle ABC?
a.
b.
c.
d.
112
477
360
227
____ 20. Solve for the unknown part of the triangle, if it exists. If b = 60, a = 82, and A = 115°, then what does B = ?
a.
b.
c.
d.
41°30’
36°14’
58°20’
75°08’
____ 21. Solve for the unknown part of the triangle, if it exists. If a = 26, b = 41, and B = 73° 10', then what does C = ?
a.
b.
c.
d.
58° 20'
54° 10'
69° 30'
65° 20'
____ 22. x = log3 200. An intermediate step is
a.
b.
c.
log10 3 · 200
d.
200 log10 3
____ 23. log 9 =
x
;x=
a.
b.
c.
d.
81
27
729
____ 24. Change (
a.
2
b.
− i)(1 − i) to polar form.
(cos 285° + i sin 285°)
(cos 285° + i sin 285°)
c.
2
(cos 85° + i sin 85°)
d.
3
(cos 285° − i sin 285°)
____ 25. Change each number to algebraic form: 4(cos 120° + i sin 120°)
a.
2
+ 2i
b.
2 + 2i
c.
–2 + 2i
d.
–2 − 2i
____ 26. Solve for the unknown part of the triangle, if it exists. If b = 125, c = 178, and C = 113°, then what does a = ?
a.
b.
c.
d.
150
122
61
87
____ 27. Evaluate the expression: log3 200
a.
b.
c.
d.
3.475
2.381
4.823
0.207
____ 28. Find x such that i + 3j and 2i + xj are perpendicular to each other.
a.
b.
c.
d.
____ 29. Express
a.
b.
c.
d.
log 7 +
log 5 − 7log 11 as a single logarithm.
____ 30. Perform the indicated operation, leave the answers in the rectangular form a + bi.
(3 + 4i) (5 – 2i)
a.
b.
c.
d.
7 + 14 i
23 + 14 i
7 + 26 i
23 + 26 i
____ 31. Find the cube roots of 1 + i. Leave the answers in polar form. What is one answer?
a.
b.
c.
d.
____ 32. What is one of the three pairs of polar coordinates for the point (5, –60°) with –360° < Θ ≤ 360°?
a.
b.
c.
d.
(–5, –240°)
(–5, –300°)
(–5, –60°)
(–5, –120°)
____ 33. A vector 10 inches in length forms angles of 32° and 48° with two component vectors. Find the magnitudes
of the two vectors. The magnitude of the other vector = ?
a.
b.
c.
d.
15 inches
7.5 inches
4.3 inches
1.9 inches
____ 34. Solve 16x = 4
a.
b.
c.
1
2
d.
____ 35. Change the polar coordinates (4, 120°) to rectangular coordinates.
a.
(–2
, 2i)
b.
(–2, 2i
c.
(2
d.
(2, –2i
)
, –2i)
)
____ 36. Find the dot product of the given vectors:
= 3i + 4j
= 4i − 3j
a.
b.
c.
d.
0
12
−12
1
____ 37. Use logarithms to evaluate
a.
b.
c.
d.
. What is the logarithm of the answer?
7.0188 – 10
8.0188 – 10
7.5342 – 10
6.5341 – 10
____ 38. Transform from rectangular coordinates to polar coordinates: (–1, −
a.
b.
(2, 240°)
(
, 60°)
c.
d.
(-2, 30°)
(2, 60°)
____ 39. log10 (x – 3) + log10 (x – 1) = log10 (2x – 5). x =
a.
b.
c.
d.
4
2
4,2
8, 1
____ 40. Change 8 (cos 150° + i sin 150°) to rectangular form.
a.
–4 + 4i
b.
4 − 4i
c.
–4
d.
4
+ 4i
+ 4i
____ 41. x = log3 4; x = .
a.
b.
c.
d.
1.3
.29
3.5
.79
____ 42. Find the indicated product. Leave the answer in polar form.
6 (cos 38° + i sin 38°) x 3 (cos 62° + i sin 62°)
a.
b.
c.
d.
9 (cos 24° + i sin 24°)
18 (cos 100° + i sin 100°)
9 (cos 100° + i sin 100°)
18 (cos 24° + i sin 24°)
)
____ 43. Perform the indicated operation, leave the answers in the rectangular form a + bi.
(3 + 9i) – (4 – 7i)
a.
b.
c.
d.
−1 + 16i
7 + 2i
−1 – 2i
7 + 16i
____ 44. Use logarithms to evaluate
a.
b.
c.
d.
. What is the answer?
2.741
9.994
1.830
5.438
____ 45. Two vectors 5 and 8 centimeters in length form an angle of 65° with each other. What is the magnitude of
the resultant vector?
a.
b.
c.
d.
9.4 cm
7.6 cm
11.1 cm
10 cm
____ 46. Perform the indicated operation, leave the answers in the rectangular form a + bi.
a.
b.
c.
d.
____ 47. Given that
a.
b.
c.
d.
= 5i − 12j, and
+
.
11 i – 20 j
11 i – 4 j
–i–4j
– i – 20 j
____ 48. Use logarithms to evaluate
a.
b.
c.
d.
= 6i − 8j, find
0.0876
0.4379
9.3319 − 10
9.6521 − 10
. What is the logarithm of the answer?
____ 49. Solve for the unknown part of the triangle, if it exists. If a = 22, b = 31, and c = 40, then what does B = ?
a.
b.
c.
d.
34° 30'
33° 10'
50° 24'
63° 0'
____ 50. Solve the equation for x and y: x − y + i = 3 + (y − 2x)i
a.
b.
c.
d.
x = −4, y = −7
x = 4, y = 7
x = 3, y = −2
x = −4, y =
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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Precalculus 2: Trigonometry
Summary of Formulas
Functions of the sum and difference of two angles:
cos (A – B) = cos A cos B + sin A sin B
cos (A + B) = cos A cos B – sin A sin B
sin (A + B) = sin A cos B + cos A sin B
sin (A – B) = sin A cos B – cos A sin B
tan A + tan B
tan (A + B) = 1 – tan A tan B
tan A – tan B
tan (A – B) = 1 + tan A tan B
Functions of twice an angle (double-angle formulas):
cos 2A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1
sin 2A = 2 sin A cos A
tan 2A =
2 tan A
1 – tan2 A
Functions of half an angle (half-angle formulas):
Tables
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Product formulas:
2 sin A cos B = sin (A + B) + sin (A – B)
2 cos A sin B = sin (A + B) – sin (A – B)
2 cos A cos B = cos (A + B) + cos (A – B)
2 sin A sin B = cos (A – B) – cos (A + B)
Sum formulas:
Tables
Included in this section are three sets of tables. The first is the Table of Trigonometric Functions for
angles written in degrees. The second is the Table of Trigonometric Functions for angles written in
radians. The third table is a table of Logarithmic Functions.
Tables
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Tables
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Tables
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Tables
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Tables
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Tables
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Tables
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Tables
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Tables
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Table 3 - Logarithms of Numbers
Tables
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Tables
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