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1. Which of these is a complex fourth root of cos 120° + i sin 120°?
A. cos 190° + i sin 190°
B. cos 210° + i sin 210°
C. cos 200° + i sin 200°
D. cos 220° + i sin 220°
2. Write the complex number 12 − 16i in polar form. Express the argument in degrees.
A. 20(cos 233.1° + i sin 233.1°)
B. 20(cos 126.9° + i sin 126.9°)
C. 20(cos 306.9° + i sin 306.9°)
D. 20(cos 53.1° + i sin 53.1°)
3. Solve the triangle with the figure shown below. Round lengths and angle measures to the nearest tenth.
A. A =32.1°, B = 20.7°, C = 127.2°
B. A = 127.2°, B = 20.7°, C = 32.1°
C. A = 127.2°, B = 32.1°, C = 20.7°
D. A = 32.1°, B = 127.2°, C = 20.7°
4. Use Demoivre's Theorem to find the indicated power of the complex number below. Write the answer in rectangular form.
(cos 30° + i sin 30°)24
A. −1
B. i
C. −i
D. 1
5. Solve the triangle in the figure below.
A. B = 55°, a = 6.55, c = 8.25
B. B = 50°, a = 8.25, c = 6.55
C. B = 60°, a = 6.55, c = 8.25
D. B = 55°, a = 8.25, c = 6.55
6. Use Heron's formula to find the area of a triangle in which a = 16 yards, b = 13 yards, and c = 16 yards. Round to the nearest square unit.
A. 101 square yards
B. 104 square yards
C. 98 square yards
D. 95 square yards
7. Two sides and an angle (SSA) of a triangle are given below. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree.
A = 30°, a = 22, b = 44
A. B = 60°, C = 60°, c = 38.1
B. B = 60°, C = 90°, c = 38.1
C. B = 90°, C = 60°, c = 38.1
D. No triangle
8. A surveyor standing 52 meters from the base of a building measures the angle to the top of the building and finds it to be 35°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it's 50°. How tall is the radio tower?
A. 13.93 meters
B. 25.56 meters
C. 9.17 meters
D. 10.01 meters
9. Use a polar coordinate system to plot the point with polar coordinates of .
10. Use the vectors below to find the specified scalar.
u = −8i + 5j and v = −11i − 6j; Find u • v.
A. 58
B. 118
C. −30
D. 88
11. The rectangular coordinates of a point are given below. Find polar coordinates of the point.
12. Find the angle between the vector 2i + 3j and the vector i − 5j.
13. Convert the rectangular equation y = 1 to a polar equation that expresses r in terms of θ.
A. r = 1
B. sin θ =1
C. r cos θ = 1
D. r sin θ = 1
14. Use Heron's formula to find the area of a triangle in which a = 19 yards, b = 19 yards, and c = 14 yards.
A. 133 square yards
B. 124 square yards
C. 130 square yards
D. 127 square yards
15. Find the product of the complex numbers below.
16. Convert the polar equation r = 4 csc θ to a rectangular equation.
A. x = 4
B. y2 = 4
C. x2 + y2 = 4
D. y = 4
17. Graph the polar equation r = 1 + sin θ.
A.
B.
C.
D.
18. Use the given vectors below to find the scalar u • v.
u = −8i + 5j and v = −15i − 8j
A. 160
B. 80
C. 120
D. −40
19. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.
v = 3i + 2j, w = 2i − 3j
A. Parallel
B. Not enough information
C. Neither orthogonal nor parallel
D. Orthogonal
20. Use the dot product to determine whether the vectors below are parallel, orthogonal, or neither.
v = 4i + 3j and w = 3i − 4j
A. Neither orthogonal nor parallel
B. Orthogonal
C. Not enough information
D. Parallel
