Honors Precalculus Final Exam Review B
ACE TRIG Final EXAM REVIEW
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____ 1. Change [pic] to degrees, minutes, and seconds.
|a. |250° 19´ 20´´ |c. |250° 20´ 20´´ |
|b. |[pic] 31´ 12´´ |d. |250° 17´ 19´´ |
____ 2. Write [pic]° [pic]´ [pic]´´ as a decimal to the nearest thousandth.
|a. |[pic]° |c. |[pic]° |
|b. |[pic]° |d. |[pic]° |
____ 3. Find the least positive angle measurement that is coterminal with [pic]°.
|a. |[pic]° |c. |[pic]° |
|b. |[pic]° |d. |[pic]° |
____ 4. Change 3.94 radians to degree measure. Round to the nearest tenth.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 5. Change [pic] to radian measure in terms of π.
|a. |[pic][pic] |c. |[pic][pic] |
|b. |[pic][pic] |d. |[pic][pic] |
____ 6. Find the polar coordinates of ([pic], 6) for r > 0.
|a. |(12, [pic]) |c. |([pic], 12) |
|b. |(–12, [pic]) |d. |(6, [pic]) |
____ 7. Find the rectangular coordinates of [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 8. Determine the polar form of the complex number [pic]. Express the angle θ in degrees, where [pic], and round numerical entries in the answer to two decimal places.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 9. Write [pic] in standard form [pic] Round numerical entries in the answer to two decimal places.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 10. Given [pic] and [pic] find and simplify [pic] Round numerical entries in the answer to two decimal places.
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 11. Find [pic]. Express the result in rectangular form.
|a. |9i |c. |6i |
|b. |8i |d. |7i |
_____ 12. Find the position vector for the vector having initial point P and terminal point Q.
P = (0, 0, 0) and Q = (2, -2, -3)
|a. |v = -2i + 2j + 3k |c. |v = 2i - 2j + 3k |
|b. |v = 2i - 2j - 3k |d. |v = -3i - 2j + 2k |
____ 13. Find the position vector for the vector having initial point P and terminal point Q.
P = (4, 2, -4) and Q = (2, 0, 1)
|a. |v = -2i - 2j + 5k |c. |v = 6i - 2j - 5k |
|b. |v = 2i + 2j - 5k |d. |v = -3i - 2j + 6k |
____ 14. Find [pic].
v = 3i + 4j + 2k
|a. |[pic] |c. |[pic] |
|b. |3 |d. |5 |
____ 15. Find [pic].
v = -3i - 6j + 3k
|a. |3[pic] |c. |6 |
|b. |3[pic] |d. |2[pic] |
____ 16. Perform the indicated operation.
v = 5i - 6j - 3k and w = 3i - 4j - 2k
Find 3v + 2w.
|a. |8i - 10j - 5k |c. |18i - 22j - 11k |
|b. |11i - 14j - 7k |d. |21i - 26j - 13k |
____ 17. Find the dot product v • w.
v = i + j and w = i + j - k
|a. |2 |c. |1 |
|b. |-2 |d. |3 |
____ 18. Find the dot product v • w.
v = 2i + j + 3k and w = i + 2j - 2k
|a. |-6 |c. |2 |
|b. |-7 |d. |-2 |
____ 19. Find the indicated cross product.
v = -4i + 2j + k, w = -6i + 5j - k
Find v × w.
|a. |3i + 2j - 32k |c. |7i + 10j + 22k |
|b. |-7i - 10j - 8k |d. |-8i + 7j + 10k |
____ 20. Find the indicated cross product.
v = 5i + 2j, w = 2i - 2j - 3k
Find v × w.
|a. |-14i + 6j - 15k |c. |-6i + 15j - 14k |
|b. |-6i + 15j - 6k |d. |-6i - 6j + 14k |
Short Answer
21. Find the least positive angle measurement that is coterminal with [pic].
22. In right triangle ABC, A = 15°, c = 37, and ∠C is the right angle. Solve the triangle. Round to the nearest tenth, if necessary.
23. Find sec 47° to four decimal places.
24. Solve triangle ABC given that A = [pic]°, B = [pic]°, and b = 12.
25. Given a triangle with b = [pic], c = [pic] , and A = [pic]°, what is the length of a? Round to the nearest tenth.
26. Change [pic] radians to degree measure.
27. Change [pic] to radian measure in terms of [pic]
28. Verify that [pic] is an identity.
29. Verify that [pic] is an identity.
30. Verify that [pic] is an identity.
31. Graph the polar equation [pic] Graph r=5.
32. Find the polar coordinates of (–6, [pic]) for r > 0.
33. Find the rectangular coordinates of [pic].
34. Find the product. Then express the result in rectangular form.
[pic]
35. Find [pic]. Express the result in rectangular form.
36. If two vectors are orthogonal, what will their dot product equal?
37. Find the inverse of y= cos 3x.
38. Evaluate sin(Cos-1 ½ )
Graph. State the amplitude, period, phase shift, and vertical translation as applicable.
39. y = tan x 40. y = cot x 41. y = sec x 42 y = csc x
43. [pic] 44. [pic]
45. Write the equation of this graph.
[pic]
Use the following for 46-49
[pic]
46. cos(x+z) 47. tan(x+z) 48. cos 2x 49. sin 2x
Find general solution in terms of k and find all solutions between 0 and 360.
50. [pic]
51. [pic]
52. [pic]
53. A model rocket is fired from ground level with an initial velocity of 80 feet per second at a launch angle of 75°.
Write the parametric equation.
How far horizontally will the rocket have traveled in 1.5 seconds?
How long will it take the rocket to land?
54. A tree casts a 45 foot shadow. The angle of elevation of the sun is 57°. Sketch a picture. Label the angle of elevation.
55. Resolve a vector with magnitude 10 and direction 220° with the horizontal into horizontal and vertical components.
56. Write the slope-intercept equation of the line with these parametric equations:
x= t+5 y= 4t -1
Honors Precalculus Final Exam Review B
Answer Section
MULTIPLE CHOICE
1. ANS: B OBJ: 5-1.1 Convert decimal degree measures to degrees¸ minutes¸ and seconds.
STO: IN PC.4 TOP: Convert decimal degree measures to degrees¸ minutes¸ and seconds.
KEY: Angle Measures, Degree Measures
2. ANS: C OBJ: 5-1.1 Convert decimal degree measures to degrees¸ minutes¸ and seconds.
STO: IN PC.4 TOP: Convert decimal degree measures to degrees¸ minutes¸ and seconds.
KEY: Angle Measures, Degree Measures
3. ANS: A OBJ: 5-1.4 Identify angles that are coterminal with a given angle.
TOP: Identify angles that are coterminal with a given angle. KEY: Coterminal Angles
4. ANS: C OBJ: 6-1.1 Change radian measures to degree measures.
STO: IN PC.4.2, IN PC.4 TOP: Change radian measures to degree measures.
KEY: Angle Measures, Degree Measures, Radian Measures
5. ANS: C OBJ: 6-1.2 Change degree measures to radian measures.
STO: IN PC.4.2, IN PC.4 TOP: Change degree measures to radian measures.
KEY: Angle Measures, Degree Measures, Radian Measures
6. ANS: C OBJ: 6-2.1 Find linear and angular velocity.
TOP: Find linear and angular velocity. KEY: Linear Velocity, Angular Velocity
7. ANS: A OBJ: 9-3.1 Convert from rectangular coordinates to polar coordinates.
STO: IN PC.6.1 TOP: Convert from rectangular coordinates to polar coordinates.
KEY: Rectangular Coordinates, Polar Coordinates
8. ANS: C OBJ: 9-3.2 Convert from polar coordinates to rectangular coordinates.
STO: IN PC.6.1 TOP: Convert from polar coordinates to rectangular coordinates.
KEY: Polar Coordinates, Rectangular Coordinates
9. ANS: C OBJ: 9-6.2 Convert complex numbers from rectangular form to polar form.
STO: IN PC.6.4 TOP: Convert complex numbers from rectangular form to polar form.
KEY: Complex Numbers, Rectangular Form, Polar Form
10. ANS: C OBJ: 9-6.3 Convert complex numbers from polar form to rectangular form.
TOP: Convert complex numbers from polar form to rectangular form.
KEY: Complex Numbers, Rectangular Form, Polar Form
11. ANS: B OBJ: 9-7.1 Find the product and quotient of complex numbers in polar form.
TOP: Find the product and quotient of complex numbers in polar form.
KEY: Multiply Complex Numbers, Divide Complex Numbers, Complex Numbers, Polar Form
12. ANS: B
OBJ: 9-8.1 Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
STO: IN PC.6.5
TOP: Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
KEY: Powers of Complex Numbers, Roots of Complex Numbers, Polar Form, De Moivre's Theorem
SHORT ANSWER
13. ANS:
[pic]
OBJ: 5-1.4 Identify angles that are coterminal with a given angle.
TOP: Identify angles that are coterminal with a given angle. KEY: Coterminal Angles
14. ANS:
B = 75°, a = 9.6, b = 35.7
OBJ: 5-5.3 Solve right triangles. STO: IN PC.3 TOP: Solve right triangles.
KEY: Right Triangles, Solve Right Triangles
15. ANS:
A = 75°, b = 3.6, c = 13.5
OBJ: 5-5.3 Solve right triangles. STO: IN PC.3 TOP: Solve right triangles.
KEY: Right Triangles, Solve Right Triangles
16. ANS:
[pic]
OBJ: 5-6.1 Solve triangles by using the Law of Sines if the measures of two angles and a side are given.
STO: IN PC.3.2, IN PC.3
TOP: Solve triangles by using the Law of Sines if the measures of two angles and a side are given.
KEY: Solve Triangles, Law of Sines
17. ANS:
15
OBJ: 5-8.1 Solve triangles using the Law of Cosines. STO: IN PC.3.1, IN PC.3.2, IN PC.3
TOP: Solve triangles using the Law of Cosines. KEY: Solve Triangles, Law of Cosines
18. ANS:
[pic]
OBJ: 6-1.1 Change radian measures to degree measures. STO: IN PC.4.2, IN PC.4
TOP: Change radian measures to degree measures.
KEY: Angle Measures, Degree Measures, Radian Measures
19. ANS:
[pic]
OBJ: 6-1.2 Change degree measures to radian measures. STO: IN PC.4.2, IN PC.4
TOP: Change degree measures to radian measures.
KEY: Angle Measures, Degree Measures, Radian Measures
20. ANS:
145.77 cm/s
OBJ: 6-2.1 Find linear and angular velocity. TOP: Find linear and angular velocity.
KEY: Linear Velocity, Angular Velocity
21. ANS:
[pic]
OBJ: 7-2.1 Use the basic trigonometric identities to verify other identities.
STO: IN PC.5.2, IN PC.5
TOP: Use the basic trigonometric identities to verify other identities.
KEY: Trigonometric Identities, Verify Identities
22. ANS:
[pic]
OBJ: 7-2.1 Use the basic trigonometric identities to verify other identities.
STO: IN PC.5.2, IN PC.5
TOP: Use the basic trigonometric identities to verify other identities.
KEY: Trigonometric Identities, Verify Identities
23. ANS:
[pic]
OBJ: 7-2.1 Use the basic trigonometric identities to verify other identities.
STO: IN PC.5.2, IN PC.5
TOP: Use the basic trigonometric identities to verify other identities.
KEY: Trigonometric Identities, Verify Identities
24. ANS:
[pic]
OBJ: 9-1.2 Graph simple polar equations. STO: IN PC.6.3
TOP: Graph simple polar equations. KEY: Polar Equations, Graph Polar Equations
25. ANS:
(12, [pic])
OBJ: 9-3.1 Convert from rectangular coordinates to polar coordinates.
STO: IN PC.6.1 TOP: Convert from rectangular coordinates to polar coordinates.
KEY: Rectangular Coordinates, Polar Coordinates
26. ANS:
[pic]
OBJ: 9-3.2 Convert from polar coordinates to rectangular coordinates.
STO: IN PC.6.1 TOP: Convert from polar coordinates to rectangular coordinates.
KEY: Polar Coordinates, Rectangular Coordinates
27. ANS:
[pic] –3–3[pic]i
OBJ: 9-7.1 Find the product and quotient of complex numbers in polar form.
TOP: Find the product and quotient of complex numbers in polar form.
KEY: Multiply Complex Numbers, Divide Complex Numbers, Complex Numbers, Polar Form
28. ANS:
–16 + 16i
OBJ: 9-8.1 Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
STO: IN PC.6.5
TOP: Find powers and roots of complex numbers in polar form using De Moivre's Theorem.
KEY: Powers of Complex Numbers, Roots of Complex Numbers, Polar Form, De Moivre's Theorem
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