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MATH1720FinalCalebWilford

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
If u = mc001-1.jpg, v = mc001-2.jpg, and w = mc001-3.jpg, evaluate u · w + v · w.
a.
-34
c.
-43
b.
-39
d.
-32
 

 2. 
To find the distance AB across a river, a distance BC =  346 m is laid off on one side of the river.  It is found that B =  115.1° and C =  13.6°. Find AB rounded to the nearest meter.
a.
83 m
c.
107 m
b.
104 m
d.
80 m
 

 3. 
If u = mc003-1.jpg and v = mc003-2.jpg, evaluate (2u) · v.
a.
62
c.
22
b.
26
d.
32
 

 4. 
A hot-air balloon is rising vertically  10 ft/sec while the wind is blowing horizontally at  4 ft/sec.  Find the angle that the balloon makes with the horizontal.
a.
34.3°
c.
52.8°
b.
68.2°
d.
21.8°
 

 5. 
Write the complex number in rectangular form.
 3mc005-1.jpg
a.
mc005-2.jpg + mc005-3.jpgi
c.
mc005-6.jpg + i
b.
mc005-4.jpg + mc005-5.jpgi
d.
mc005-7.jpg + mc005-8.jpgi
 

 6. 
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 distance from the object to the closest point of observation is given by
D = mc006-1.jpg ft.
Find B if mc006-2.jpg mc006-3.jpg and mc006-4.jpg Give your answer in degrees to the nearest hundredth.
a.
51.00°
c.
64.09°
b.
72.05°
d.
61.64°
 

 7. 
The figure shows an angle è in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of è.
Find sec è.
mc007-1.jpg
a.
- mc007-2.jpg
c.
mc007-4.jpg
b.
- mc007-3.jpg
d.
mc007-5.jpg
 

 8. 
Find sum of the pair of complex numbers.
 2  + 6i,  -4
a.
2  + 2i
c.
-2  + 6i
b.
4
d.
2  + 10i
 

 9. 
Simplify the power of i.
 mc009-1.jpg
a.
-i
c.
-1
b.
i
d.
1
 

 10. 
Give the degree measure of è.
è = arcsin mc010-1.jpg
a.
315°
c.
300°
b.
30°
d.
-30°
 

 11. 
Find the component form of the indicated vector.
 Let u = mc011-1.jpg, v = mc011-2.jpg. Find  -4u +  2v.
a.
mc011-3.jpg
c.
mc011-5.jpg
b.
mc011-4.jpg
d.
mc011-6.jpg
 

 12. 
Solve the equation for exact solutions over the interval [0, 2ð).  cos2x + 2 cos x + 1 = 0
a.
{ð}
c.
mc012-2.jpg
b.
mc012-1.jpg
d.
{2ð}
 

 13. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc013-1.jpg
b - c
a.
mc013-2.jpg
b.
mc013-3.jpg
 

 14. 
Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°].
mc014-1.jpg
a.
5;  233.1°
c.
7;  216.9°
b.
5;  36.9°
d.
5;  216.9°
 

 15. 
y = mc015-1.jpg( -1)
a.
2ð
c.
mc015-3.jpg
b.
- mc015-2.jpg
d.
ð
 

 16. 
Use Identities to find the exact value.  cos mc016-1.jpg
a.
mc016-2.jpg
c.
mc016-4.jpg + mc016-5.jpg
b.
mc016-3.jpg
d.
mc016-6.jpg - mc016-7.jpg
 

 17. 
Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.

mc017-1.jpg
a.
mc017-2.jpg
c.
mc017-4.jpg
b.
mc017-3.jpg
d.
mc017-5.jpg
 

 18. 
True or false? The statement tan(tan-1 x) = x for all real numbers in the interval  0 = x = ð.
a.
True
b.
False
 

 19. 
Two forces of  425 newtons and  267 newtons act at a point.  The resultant force is  507 newtons. Find the angle between the forces.
a.
163.7°
c.
52.7°
b.
91.3°
d.
88.7°
 

 20. 
Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
4 sin2è = 3
a.
{60°, 120°}
c.
{240°, 300°}
b.
Ø
d.
{60°, 120°, 240°, 300°}
 

 21. 
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a =  6.3 in.
b =  13.6 in.
c =  15.3 in.
a.
A =  24.3°, B =  62.6°, C =  93.1°
c.
No triangle satisfies the given conditions.
b.
A =  26.3°, B =  60.6°, C =  93.1°
d.
A =  22.3°, B =  62.6°, C =  95.1°
 

 22. 
Find the dot product for the pair of vectors.
 5i -  4j, 8i + j
a.
44
c.
36
b.
-27
d.
0
 

 23. 
y =  tan-1 ( -1)
a.
mc023-1.jpg
c.
mc023-3.jpg
b.
mc023-2.jpg
d.
mc023-4.jpg
 

 24. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
mc024-1.jpg
a.
real
c.
real, complex
b.
complex, nonreal complex
d.
complex, pure imaginary
 

 25. 
The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0.  Determine the equation of the graph.

mc025-1.jpg
a.
y =  2 cos mc025-2.jpg
c.
y =  5 sin mc025-3.jpg
b.
y =  5 cos ( 2x)
d.
y =  5 sin ( 2x)
 

 26. 
Find the component form of the indicated vector.
 Let u = mc026-1.jpg. Find  -7u.
a.
mc026-2.jpg
c.
mc026-4.jpg
b.
mc026-3.jpg
d.
mc026-5.jpg
 

 27. 
Find the area of a triangular-shaped field with sides of  188.7 m and  197.5 m, and the included angle between them measuring mc027-1.jpg Round to the nearest square meter.
a.
34,328 m2
c.
14,508 m2
b.
17,164 m2
d.
7254 m2
 

 28. 
Write the complex number in trigonometric form r(cos è + i sin è), with è in the interval [0°, 360°).
9 +  9i
a.
9mc028-1.jpg(cos 135° + i sin 135°)
c.
9mc028-3.jpg(cos 45° + i sin 45°)
b.
9mc028-2.jpg(cos 315° + i sin 315°)
d.
9mc028-4.jpg(cos 225° + i sin 225°)
 

 29. 
Find the angle between the pair of vectors to the nearest tenth of a degree.  5i -  4j,  2i -  6j
a.
60.4°
c.
32.9°
b.
33.9°
d.
110.2°
 

 30. 
The figure shows an angle è in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of è.
Find tan è.
mc030-1.jpg
a.
mc030-2.jpg
c.
- mc030-4.jpg
b.
- mc030-3.jpg
d.
- mc030-5.jpg
 

 31. 
Use a sum or difference identity to find the exact value.
sin(-15°)
a.
mc031-1.jpg
c.
mc031-3.jpg
b.
mc031-2.jpg
d.
mc031-4.jpg
 

 32. 
Indicate whether the statement is true always, sometimes, or never.
The product of a pair of complex conjugates is a real number.
a.
Never
c.
Sometimes
b.
Always
 

 33. 
Use an identity to write the expression as a single trigonometric function or as a single number.
 mc033-1.jpg
a.
mc033-2.jpg
c.
mc033-4.jpg
b.
mc033-3.jpg
d.
mc033-5.jpg
 

 34. 
Write the number as the product of a real number and i.
mc034-1.jpg
a.
-5imc034-2.jpg
c.
5imc034-4.jpg
b.
-5mc034-3.jpg
d.
5mc034-5.jpg
 

 35. 
Find the missing parts of the triangle.
A =  97.3°
b = 15.2 ft
a =  30.7 ft
If necessary, round angles and side lengths to the nearest tenth.
a.
B =  53.3°, C =  29.4°, c =  24.8 ft
c.
no such triangle
b.
B =  34.4°, C =  48.3°, c =  24.8 ft
d.
B =  29.4°, C =  53.3°, c =  24.8 ft
 

 36. 
Determine the number of triangles ABC possible with the given parts.
a = 24, b =  21, A =  47°
a.
1
c.
3
b.
2
d.
0
 

 37. 
It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port? Round to the nearest tenth of a kilometer.
a.
2.7 km
c.
3.5 km
b.
3.7 km
d.
3.1 km
 

 38. 
A force of  38 lb is required to hold a  66 lb toolbox on an incline. What angle does the incline make with the horizontal?
a.
73.3°
c.
35.2°
b.
16.7°
d.
54.8°
 

 39. 
Use the figure to find the specified vector.
Find a + b.
mc039-1.jpg
a.
mc039-2.jpg
c.
mc039-4.jpg
b.
mc039-3.jpg
d.
mc039-5.jpg
 

 40. 
Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for ð.
 39.3222°
a.
0.5863
c.
0.7863
b.
0.8863
d.
0.6863
 

 41. 
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
 (1 + cot è)(1 - cot è) - mc041-1.jpg è
a.
2
c.
2 mc041-3.jpg è
b.
-2 mc041-2.jpg è
d.
0
 

 42. 
Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
 a =  46 ft
b =  54 ft
c =  62 ft
a.
1508 mc042-1.jpg
c.
1206 mc042-3.jpg
b.
134 mc042-2.jpg
d.
1809 mc042-4.jpg
 

 43. 
Two people are carrying a box.  One person exerts a force of  129 pounds at an angle of  49.4° with the horizontal.  The other person exerts a force of  98 pounds at an angle of  52.4°.  Find the weight of the box.
a.
104 lb
c.
266 lb
b.
227 lb
d.
177 lb
 

 44. 
Vector v has the given magnitude and direction. Find the horizontal or vertical component of v, as indicated, if è is the direction angle of v from the horizontal. Round to the nearest tenth when necessary.
á =  46.7°, |v| =  86.5;  Find the horizontal component of v.
a.
59.3
c.
122.3
b.
63
d.
3.7
 

 45. 
sec mc045-1.jpg
a.
-2
c.
-mc045-3.jpg
b.
mc045-2.jpg
d.
- mc045-4.jpg
 

 46. 
Find the indicated angle or side. Give an exact answer.
Find the measure of angle A in degrees.
mc046-1.jpg
a.
30°
c.
60°
b.
45°
d.
75°
 

 47. 
A painting 1 meter high and 3 meters from the floor will cut off an angle è to an observer, where mc047-1.jpg assuming that the observer is x feet from the wall where the painting is displayed and that the eyes of the observer are  1.6 meters above the ground (see the figure). Find the value of è for mc047-2.jpg Round to the nearest tenth of a degree.
mc047-3.jpg
a.
18.3°
c.
13.3°
b.
15.8°
d.
33.1°
 

 48. 
mc048-1.jpg

Find sin A.
a.
sin A = mc048-2.jpg
c.
sin A = mc048-4.jpg
b.
sin A = mc048-3.jpg
d.
sin A = mc048-5.jpg
 

 49. 
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for ð.
 5
a.
572.66°
c.
286.48°
b.
572.96°
d.
286.78°
 

 50. 
Without using a calculator, give the exact trigonometric function value with rational denominator.
cos 30°
a.
mc050-1.jpg
c.
mc050-3.jpg
b.
mc050-2.jpg
d.
mc050-4.jpg
 

 51. 
Use the fundamental identities to find the value of the trigonometric function.
Find sin è if cos è = mc051-1.jpg and è is in quadrant IV.
a.
mc051-2.jpg
c.
- mc051-4.jpg
b.
- mc051-3.jpg
d.
mc051-5.jpg
 

 52. 
Find the missing parts of the triangle.
B =  29.5°
b =  19.45
a =  19.75
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.
a.
no such triangle
b.
A =  150°, C =  0.5°, c =  0.34
c.
A =  30°, C =  120.5°, c =  34.03
d.
mc052-1.jpg =  30°, mc052-2.jpg =  120.5°, mc052-3.jpg =  34.03;
mc052-4.jpg =  150°, mc052-5.jpg =  0.5°, mc052-6.jpg =  0.34
 

 53. 
Graph the complex number.
 -4 - i
mc053-1.jpg
a.
mc053-2.jpg
c.
mc053-4.jpg
b.
mc053-3.jpg
d.
mc053-5.jpg
 

 54. 
mc054-1.jpg
     
A)                                                                  B)
      mc054-2.jpg                  mc054-3.jpg 

C)                                                                  D)
  mc054-4.jpg                  mc054-5.jpg
a.
1A, 2D, 3C, 4B
c.
1B, 2D, 3C, 4A
b.
1A, 2B, 3C, 4D
d.
1C, 2A, 3B, 4D
 

 55. 
A stained glass window is composed of 20 triangular sections, each with sides  4,  7, and  7 in.  Find the total area of the window (to the nearest square inch).
a.
268 mc055-1.jpg
c.
13 mc055-3.jpg
b.
3461 mc055-2.jpg
d.
89 mc055-4.jpg
 

 56. 
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
 C =  113.6°
a =  7.5 m
b =  9.6 m
a.
c =  17.3 m, A =  30.4°, B =  36°
c.
c =  14.4 m, A =  28.4°, B =  38°
b.
c =  20.2 m, A =  26.4°, B =  40°
d.
No triangle satisfies the given conditions.
 

 57. 
Perform the indicated operations. Simplify the answer.
 mc057-1.jpg
a.
3
c.
3i
b.
-3
d.
-3i
 

 58. 
Find the exact value by using a half-angle identity.
sin 75°
a.
mc058-1.jpg mc058-2.jpg
c.
mc058-5.jpg mc058-6.jpg
b.
- mc058-3.jpg mc058-4.jpg
d.
- mc058-7.jpg mc058-8.jpg
 

 59. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
mc059-1.jpg
a.
real, complex
c.
complex, pure imaginary
b.
pure imaginary
d.
complex, nonreal complex
 

 60. 
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
sin mc060-1.jpg cos mc060-2.jpg = mc060-3.jpg
a.
Not an identity
b.
Identity
 

 61. 
Find the corresponding angle measure in radians.
45°
mc061-1.jpg
a.
mc061-2.jpg
c.
mc061-4.jpg
b.
mc061-3.jpg
d.
mc061-5.jpg
 

 62. 
Find the exact circular function value.
sin mc062-1.jpg
a.
- mc062-2.jpg
c.
- mc062-4.jpg
b.
mc062-3.jpg
d.
mc062-5.jpg
 

 63. 
Without using a calculator, give the exact trigonometric function value with rational denominator.
 cot 45°
a.
mc063-1.jpg
c.
mc063-2.jpg
b.
1
d.
mc063-3.jpg
 

 64. 
Perform the indicated operations. Simplify the answer.
mc064-1.jpg
a.
-5i
c.
-5
b.
5i
d.
5
 

 65. 
Perform the indicated operations and simplify the result so there are no quotients.
mc065-1.jpg + mc065-2.jpg
a.
1 + cot è
c.
sec è csc è
b.
-2 tan2è
d.
sin è tan è
 

 66. 
A generator produces an alternating current according to the equation mc066-1.jpg where t is time in seconds and I is the current in amperes. What is the smallest time t such that mc066-2.jpg
a.
mc066-3.jpg sec
c.
mc066-5.jpg sec
b.
mc066-4.jpg sec
d.
mc066-6.jpg sec
 

 67. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
-7x2  - 3x  - 8 = 0
a.
mc067-1.jpg
c.
mc067-3.jpg
b.
mc067-2.jpg
d.
mc067-4.jpg
 

 68. 
True or false? The statement cos-1(cos x) = x for all real numbers in the interval  -8 = x = 8.
a.
False
b.
True
 

 69. 
Find the exact value by using a half-angle identity.
cos mc069-1.jpg
a.
mc069-2.jpg mc069-3.jpg
c.
mc069-6.jpg mc069-7.jpg
b.
- mc069-4.jpg mc069-5.jpg
d.
- mc069-8.jpg mc069-9.jpg
 

 70. 
Find the exact value of s in the given interval that has the given circular function value.
mc070-1.jpg; tan s = 1
a.
s = mc070-2.jpg
c.
s = mc070-4.jpg
b.
s = mc070-3.jpg
d.
s = mc070-5.jpg
 

 71. 
Use an identity to write the expression as a single trigonometric function or as a single number.
sin 22.5° cos 22.5°
a.
mc071-1.jpg
c.
mc071-3.jpg
b.
mc071-2.jpg
d.
mc071-4.jpg
 

 72. 
A wheel is rotating at  5 radians/sec, and the wheel has a  83-inch diameter. To the nearest foot, what is the speed of a point on the rim in ft/min?
a.
1038 ft/min
c.
1043 ft/min
b.
1033 ft/min
d.
1028 ft/min
 

 73. 
Use the formula ù = mc073-1.jpg to find the value of the missing variable. Give an exact answer unless otherwise indicated.
 è = mc073-2.jpg radian, t =  11 sec
a.
mc073-3.jpg radians per sec
c.
mc073-5.jpg radians per sec
b.
mc073-4.jpg radians per sec
d.
mc073-6.jpg radian per sec
 

 74. 
Find sum of the pair of complex numbers.
 2  + 7i,  -11i
a.
2  + 77i
c.
2  + 18i
b.
2  - 77i
d.
2  - 4i
 

 75. 
The voltage E in an electrical circuit is given by E =  1.3 cos  100ðt, where t is time measured in seconds.  Find the period.
a.
50
c.
50ð
b.
mc075-1.jpg
d.
mc075-2.jpg
 

 76. 
Use Identities to find the exact value.  cos 255°
a.
mc076-1.jpg
c.
mc076-4.jpg - mc076-5.jpg
b.
mc076-2.jpg - mc076-3.jpg
d.
mc076-6.jpg
 

 77. 
Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°].
 mc077-1.jpg
a.
14; 330°
c.
28; 150°
b.
14; 150°
d.
28; 30°
 

 78. 
Without using a calculator, give the exact trigonometric function value with rational denominator.
 sin 60°
a.
mc078-1.jpg
c.
mc078-3.jpg
b.
mc078-2.jpg
d.
mc078-4.jpg
 

 79. 
Write the complex number in rectangular form.
mc079-1.jpg cis 270°
a.
-2i
c.
-mc079-2.jpg
b.
-i
d.
-imc079-3.jpg
 

 80. 
Simplify the power of i.
mc080-1.jpg
a.
-i
c.
-1
b.
1
d.
i
 



 
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