Download Trigonometry Math 1316 Practice Exam 4 1) Write the trigonometric

Trigonometry
Math 1316
Practice Exam 4
1) Write the trigonometric expression cos (tan -1 u) as an algebraic expression in u. Hint: Use a right triangle
diagram.
u
1
1
A)
B)
C)
D) u u2 + 1
2
2
u +1
u +1
u2 - 1
2) Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
b = 5, B = 25°; Find a, c, and A.
A) a = 10.72
c = 11.83
A = 65°
B) a = 10.72
c = 12.83
A = 75°
C) a = 10.72
c = 11.83
A = 75°
D) a = 10.72
c = 12.83
A = 65°
3) Solve the triangle.
35°
120°
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A) C = 30°, a = 9.06, c = 4.42
C) C = 25°, a = 4.42, c = 9.06
B) C = 25°, a = 9.06, c = 4.42
D) C = 20°, a = 4.42, c = 9.06
4) Solve the triangle: a = 6, b = 8, C = 70°
A) c = 8.2, A = 43.5°, B = 66.5°
C) c = 10, A = 56.9°, B = 53.1°
B) c = 6.3, A = 28.6°, B = 81.4°
D) c = 9, A = 52.8°, B = 57.2°
5) Solve the triangle.
9
6
4
A) A = 127.2°, B = 32.1°, C = 20.7°
C) A = 127.2°, B = 20.7°, C = 32.1°
B) A = 32.1°, B = 20.7°, C = 127.2°
D) A = 32.1°, B = 127.2°, C = 20.7°
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6) A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the
house. How tall is the house? Round your answer to the nearest 0.1 foot.
A) 18.7 ft
B) 19 ft
C) 18.8 ft
D) 18.6 ft
7) An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west
of the airplane. They report the angles of elevation as 11° and 23°. How high is the airplane?
A) 3.67 mi
B) 1.95 mi
C) 1.79 mi
D) 0.95 mi
8) A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing
S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420
mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.
A) 1111 mi
B) 1011 mi
C) 1110 mi
D) 1010 mi
9) Match the point polar point -3, -
A) A
with either A, B, C, or D on the graph.
B) B
10) Convert the point 7,
A)
3
2
3
C) C
D) D
given in polar coordinates into rectangular coordinates.
7
7 3
,2
2
B) -
7
7 3
,2
2
C) -
7 7 3
,
2
2
D)
7 7 3
,
2
2
11) Convert the point (0, 2) given in rectangular coordinates into polar coordinates.
A) 2, -
C) 2,
B) (2, 0)
2
12) Write the rectangular equation x 2 + 4y2 = 4 in polar form.
A) cos2 + 4 sin 2 = 4r
C) 4 cos2
+ sin2
= 4r
13) Write the complex number in polar form:
A) 4 2(cos 120° + i sin 120°)
C) 4 2(cos 135° + i sin 135°)
2
B) r2 (cos 2 + 4 sin 2 ) = 4
D) r2 (4 cos2 + sin2 ) = 4
-4 + 4i
B) 16(cos 120° + i sin 120°)
D) 16(cos 135° + i sin 135°)
2
D) (2, )
14) Given the complex numbers in polar form z = 10(cos 30° + i sin 30°) and w = 5(cos 10° + i sin 10°).
Find zw.
A) 15(cos 40° + i sin 40°)
B) 50(cos 40° + i sin 40°)
C) 15(cos 300° + i sin 300°)
D) 50(cos 300° + i sin 300°)
Use the vectors in the figure below to graph the following vector.
15) u + z
A)
B)
C)
D)
3
16) If v = 3i - 5j and w = -7i + 4j, find 3v - 4w.
A) -4i - j
B) -19i + j
C) 17i - 10j
D) 37i - 31j
17) If v = 3i + 4j, find v .
A) 5
C) 7
D) 25
B)
5
18) Write the component form of vector v, given the magnitude and direction angle: v = 7, = 45°
7 3
7
7
7 3
7 2
7 2
2
2
i+ j
j
i+
j
ij
A) v =
B) v = i +
C) v =
D) v = 2
2
2
2
2
2
2
2
19) Find the dot product v · w:
A) -6
v = i + 2j, w = 8i - j
B) 6
C) 10
D) 0
20) Find the angle between the vectors v = -4i - 2j and w = -5i - 8j.
A) 41.4°
B) 15.7°
C) 5.7°
D) 31.4°
21) Which of the following vectors is parallel to v = i - j?
A) w = i + j
B) w = i - 2j
D) w = 2i + 2j
C) w = 2i - 2j
22) State whether the vectors are parallel, orthogonal, or neither: v = 4i + 3j, w = 3i - 4j
A) Parallel
B) Orthogonal
C) Neither
23) Two forces, F1 of magnitude 35 newtons (N) and F2 of magnitude 55 newtons, act on an object at angles of 45°
and -60° (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is,
find F1 + F2 . Round the direction and magnitude to two decimal places.
A) Direction: -23.65°; magnitude: 8.67 N
C) Direction: -66.35°; magnitude: 57.04 N
B) Direction: 66.35°; magnitude: 57.04 N
D) Direction: -23.65°; magnitude: 57.04 N
24) An airplane has an air speed of 550 miles per hour bearing N30°W. The wind velocity is 50 miles per hour in
the direction N30°E. To the nearest tenth, what is the ground speed of the plane? What is its direction?
A) 552.3 mph; N54.8°W
B) 526.8 mph; N55.3°W
C) 552.3 mph; N24.8°W
D) 576.6 mph; N25.7°W
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