Exam: 250313RR - Additional Topics in Trigonometry
1. Convert the rectangular equation y = 3 to a polar equation (that is, in terms of r and θ).
A. sin θ = 3
B. r cos θ = 3
C. r = 3
D. r sin θ = 3
2. A vector v has initial point P
A. v = -6i - 6j
B. v = 6i - 4j
C. v = 4i - 6j
D. v = -4i + 6j
3. A vector v has initial point P Write v in terms of ai + bj.
4. Use the dot product to determine whether the vectors below are parallel, orthogonal, or neither.
v = 4i + 3j and w = 3i - 4j
A. Not enough information
B. Orthogonal
C. Neither orthogonal nor parallel
D. Parallel
5. 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. 95 square yards
C. 104 square yards
D. 98 square yards
6. Which of these is a complex fourth root of cos 120° + i sin 120°?
A. cos 210° + i sin 210°
B. cos 220° + i sin 220°
C. cos 200° + i sin 200°
D. cos 190° + i sin 190°
7. 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 306.9° + i sin 306.9°)
C. 20(cos 53.1° + i sin 53.1°)
D. 20(cos 126.9° + i sin 126.9°)
8. Convert the polar equation r = 4 csc θ to a rectangular equation.
9. Use the given vectors below to find the scalar u • v.
u = -8i + 5j and v = -15i - 8j
A. 80
B. -40
C. 160
D. 120
10. Solve the triangle below, rounding to the nearest tenth.
A. B = 45°, a = 8.2, c = 12.7°
B. B = 40°, a = 12.7, c = 8.1°
C. B = 50°, a = 8.2, c = 12.7°
D. B = 45°, a = 12.7, c = 8.1°
11. Use the vectors below to find the specified scalar.
u = -8i + 5j and v = -11i - 6j; Find u • v.
A. 88
B. 58
C. -30
D. 118
12. 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. 124 square yards
C. 133 square yards
D. 127 square yards
13. Convert the polar equation r = 9 csc θ to a rectangular equation.
14. Find the unit vector having the same direction as v if v = 12i + 5j.
15. The rectangular coordinates of a point are given below. Find polar coordinates of the point.
16. 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 = 55°, a = 8.25, c = 6.55
D. B = 60°, a = 6.55, c = 8.25
17. 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
18. Find the product of the complex numbers below.
19. Find the absolute value of the complex number z = - 14 - 8i.
20. Use a polar coordinate system to plot the point with polar coordinates of .
