ADDITIONAL TOPICS IN TRIGONOMETRY
1. Which of these is a complex fourth root of cos 120° + i sin 120°?
A. cos 190° + i sin 190°
B. cos 200° + i sin 200°
C. cos 210° + i sin 210°
D. cos 220° + i sin 220°
2. Convert the polar equation r = 4 csc θ to a rectangular equation.
A. y 2 = 4
B. y = 4
C. x
2 + y
2 = 4
D. x = 4
3. 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
4. Use the given vectors below to find the scalar u • v.
u = -8i + 5j and v = -15i - 8j
A. 160
B. 80
C. -40
D. 120
5. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.
v = 3i + 2j, w = 2i - 3j
A. Parallel
B. Neither orthogonal nor parallel
C. Orthogonal
D. Not enough information
6. Use Heron's formula to find the area of a triangle in which a = 19 yards, b = 19 yards, and c = 14 yards.
A. 130 square yards
B. 127 square yards
C. 124 square yards
D. 133 square yards
7. Convert the rectangular equation y = 3 to a polar equation (that is, in terms of r and θ).
A. r = 3
B. r sin θ = 3
C. sin θ = 3
D. r cos θ = 3
8. Solve the triangle below.
A. B = 45°, a = 12.68, c = 8.1°
B. B = 40°, a = 12.68, c = 8.1°
C. B = 45°, a = 8.18, c = 12.6°
D. B = 50°, a = 8.18, c = 12.6°
9. A vector v has initial point P
A. v = -4i + 6j
B. v = -6i - 6j
C. v = 6i - 4j
D. v = 4i - 6j
1 = (0, 0) and terminal point P
2 = (4, -6). Write v in terms of ai + bj.
10. Two sides of 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 = 90°, c = 38.1
B. B = 60°, C = 60°, c = 38.1
C. B = 90°, C = 60°, c = 38.1
D. No triangle
11. Solve the triangle in the figure below.
A. B = 50°, a = 8.25, c = 6.55
B. B = 55°, a = 6.55, c = 8.25
C. B = 60°, a = 6.55, c = 8.25
D. B = 55°, a = 8.25, c = 6.55
12. Solve the triangle with the figure shown below. Round lengths to the nearest tenth and angle measures to the nearest degree.
A. A = 127.2°, B = 20.7°, C = 32.1°
B. A = 127.2°, B = 32.1°, C = 20.7°
C. A =32.1°, B = 20.7°, C = 127.2°
D. A = 32.1°, B = 127.2°, C = 20.7°
13. Convert the polar equation r = 9 csc θ to a rectangular equation.
A. x
2
+ y
2
= 9
B. y
2
= 9
C. y = 9
D. x = 9
14. 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. 104 square yards
B. 101 square yards
C. 98 square yards
D. 95 square yards
15. Convert the rectangular equation y = 1 to a polar equation that expresses r in terms of θ.
A. r = 1
B. r sin θ = 1
C. sin θ =1
D. r cos θ = 1