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hat is one of the three pairs of polar coordinates for the point (5, 210°) with –360° < Θ ≤ 360°?

  1. (5, 150°)
  2. (–5, 150°)
  3. (–5, –150°)
  4. (5, –150°)

Solve the triangle for the unknown parts. a = 48, B = 50°, C = 62°, c = ____

  1. 109
  2. 46
  3. 50
  4. 24

The horizontal and vertical components of a vector are 20 feet and 15 feet respectively. Find the magnitudes of the resultant vector and the angle that it forms with the horizontal. What is the magnitude?

  1. 40 feet
  2. 35 feet
  3. 25 feet
  4. 5 feet

Transform from polar coordinates to rectangular coordinates: ( page1image48751968, 45°)

  1. (1, −1)
  2. ( , )
  3. (1, 1)
  4. (−1, −1)

Use logarithms to evaluate

  1. .00342
  2. .000342
  3. .00104
  4. .0104

. What i

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Course Name: Precalculus: Trigonometry Student: Kwinda Netshitangani Course ID: MTHH044059 ID: J47865775 Submittal: 59 Progress Test 3 Progress Test 3 (Evaluation 59) covers the course materials that were assigned in Units 5 and 6. Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. You may not have access to notes or any of the course materials while you are taking the test. You may also use your graphing calculator on this test. The Summary of Formulas and Trigonometric Tables from the Appendix is included for your use during the test. ____ 1. What is one of the three pairs of polar coordinates for the point (5, 210°) with –360° < Θ ≤ 360°? a. b. c. d. ____ 2. Solve the triangle for the unknown parts. a = 48, B = 50°, C = 62°, c = ____ a. b. c. d. ____ 3. ____ 5. 109 46 50 24 The horizontal and vertical components of a vector are 20 feet and 15 feet respectively. Find the magnitudes of the resultant vector and the angle that it forms with the horizontal. What is the magnitude? a. b. c. d. ____ 4. (5, 150°) (–5, 150°) (–5, –150°) (5, –150°) 40 feet 35 feet 25 feet 5 feet Transform from polar coordinates to rectangular coordinates: ( a. b. (1, −1) ( , c. d. (1, 1) (−1, −1) ) Use logarithms to evaluate a. b. c. d. .00342 .000342 .00104 .0104 . What is the answer? , 45°) ____ 6. The horizontal and vertical components of a vector are 8 inches and 2 inches respectively. What is the angle that it forms with the horizontal? a. b. c. d. ____ 7. Given that a. b. c. d. ____ 8. = 5i − 12j, and = 6i − 8j, find 2 −3 . – 8 i – 48 j 3 i – 52 j –8i 3 i – 20 j Simplify the following: i10 a. b. c. d. ____ 9. 14° 28° 7° 45° 1 −1 i –i Given that a. b. c. d. = 3i + 4j, and = 5i − 12j, find · . 56 63 –16 –33 ____ 10. Solve for the unknown part of the triangle, if it exists. If c = 74, b = 48, and C = 74°, then what does B = ? a. b. c. d. 45°10’ 17°50’ 25°20’ 38°30’ ____ 11. Solve for the unknown part of the triangle, if it exists. If b = 60, a = 82, and A = 115°, then what does c = ? a. b. c. d. 41 36 72 12 ____ 12. 9x = 27; x = a. b. c. d. 3 ____ 13. Express as an algebraic sum of logarithms. a. log 6 + b. (log 6 + log 5 − log 51 − log 16) c. log 6 + log 5 + log 5 − log 51 + log 51 − log 16 log 16 d. ____ 14. log5 x = 3; x = a. b. c. d. 243 125 625 729 ____ 15. Given that = 2i − 3j, and = 5i + 7j, find a unit vector parallel to . a. b. c. d. ____ 16. log a. b. c. 4 = x; x = –2 2 d. ____ 17. A vector 20 inches in length forms angles of 58° and 22° with two component vectors. Find the magnitudes of the two vectors. The magnitude of one vector = ? a. b. c. d. 17.2 inches 23.2 inches 12.5 inches 18.5 inches ____ 18. Perform the indicated operation, leave the answers in the rectangular form a + bi. Simplify: 7i2 + 8i3 + 9i4 + 10i5. a. b. c. d. 16 + 2 i 2+2i 16 + 18 i 2 + 18 i ____ 19. Given a = 27, b = 36, c = 49. What is the area of triangle ABC? a. b. c. d. 112 477 360 227 ____ 20. Solve for the unknown part of the triangle, if it exists. If b = 60, a = 82, and A = 115°, then what does B = ? a. b. c. d. 41°30’ 36°14’ 58°20’ 75°08’ ____ 21. Solve for the unknown part of the triangle, if it exists. If a = 26, b = 41, and B = 73° 10', then what does C = ? a. b. c. d. 58° 20' 54° 10' 69° 30' 65° 20' ____ 22. x = log3 200. An intermediate step is a. b. c. log10 3 · 200 d. 200 log10 3 ____ 23. log 9 = x ;x= a. b. c. d. 81 27 729 ____ 24. Change ( a. 2 b. − i)(1 − i) to polar form. (cos 285° + i sin 285°) (cos 285° + i sin 285°) c. 2 (cos 85° + i sin 85°) d. 3 (cos 285° − i sin 285°) ____ 25. Change each number to algebraic form: 4(cos 120° + i sin 120°) a. 2 + 2i b. 2 + 2i c. –2 + 2i d. –2 − 2i ____ 26. Solve for the unknown part of the triangle, if it exists. If b = 125, c = 178, and C = 113°, then what does a = ? a. b. c. d. 150 122 61 87 ____ 27. Evaluate the expression: log3 200 a. b. c. d. 3.475 2.381 4.823 0.207 ____ 28. Find x such that i + 3j and 2i + xj are perpendicular to each other. a. b. c. d. ____ 29. Express a. b. c. d. log 7 + log 5 − 7log 11 as a single logarithm. ____ 30. Perform the indicated operation, leave the answers in the rectangular form a + bi. (3 + 4i) (5 – 2i) a. b. c. d. 7 + 14 i 23 + 14 i 7 + 26 i 23 + 26 i ____ 31. Find the cube roots of 1 + i. Leave the answers in polar form. What is one answer? a. b. c. d. ____ 32. What is one of the three pairs of polar coordinates for the point (5, –60°) with –360° < Θ ≤ 360°? a. b. c. d. (–5, –240°) (–5, –300°) (–5, –60°) (–5, –120°) ____ 33. A vector 10 inches in length forms angles of 32° and 48° with two component vectors. Find the magnitudes of the two vectors. The magnitude of the other vector = ? a. b. c. d. 15 inches 7.5 inches 4.3 inches 1.9 inches ____ 34. Solve 16x = 4 a. b. c. 1 2 d. ____ 35. Change the polar coordinates (4, 120°) to rectangular coordinates. a. (–2 , 2i) b. (–2, 2i c. (2 d. (2, –2i ) , –2i) ) ____ 36. Find the dot product of the given vectors: = 3i + 4j = 4i − 3j a. b. c. d. 0 12 −12 1 ____ 37. Use logarithms to evaluate a. b. c. d. . What is the logarithm of the answer? 7.0188 – 10 8.0188 – 10 7.5342 – 10 6.5341 – 10 ____ 38. Transform from rectangular coordinates to polar coordinates: (–1, − a. b. (2, 240°) ( , 60°) c. d. (-2, 30°) (2, 60°) ____ 39. log10 (x – 3) + log10 (x – 1) = log10 (2x – 5). x = a. b. c. d. 4 2 4,2 8, 1 ____ 40. Change 8 (cos 150° + i sin 150°) to rectangular form. a. –4 + 4i b. 4 − 4i c. –4 d. 4 + 4i + 4i ____ 41. x = log3 4; x = . a. b. c. d. 1.3 .29 3.5 .79 ____ 42. Find the indicated product. Leave the answer in polar form. 6 (cos 38° + i sin 38°) x 3 (cos 62° + i sin 62°) a. b. c. d. 9 (cos 24° + i sin 24°) 18 (cos 100° + i sin 100°) 9 (cos 100° + i sin 100°) 18 (cos 24° + i sin 24°) ) ____ 43. Perform the indicated operation, leave the answers in the rectangular form a + bi. (3 + 9i) – (4 – 7i) a. b. c. d. −1 + 16i 7 + 2i −1 – 2i 7 + 16i ____ 44. Use logarithms to evaluate a. b. c. d. . What is the answer? 2.741 9.994 1.830 5.438 ____ 45. Two vectors 5 and 8 centimeters in length form an angle of 65° with each other. What is the magnitude of the resultant vector? a. b. c. d. 9.4 cm 7.6 cm 11.1 cm 10 cm ____ 46. Perform the indicated operation, leave the answers in the rectangular form a + bi. a. b. c. d. ____ 47. Given that a. b. c. d. = 5i − 12j, and + . 11 i – 20 j 11 i – 4 j –i–4j – i – 20 j ____ 48. Use logarithms to evaluate a. b. c. d. = 6i − 8j, find 0.0876 0.4379 9.3319 − 10 9.6521 − 10 . What is the logarithm of the answer? ____ 49. Solve for the unknown part of the triangle, if it exists. If a = 22, b = 31, and c = 40, then what does B = ? a. b. c. d. 34° 30' 33° 10' 50° 24' 63° 0' ____ 50. Solve the equation for x and y: x − y + i = 3 + (y − 2x)i a. b. c. d. x = −4, y = −7 x = 4, y = 7 x = 3, y = −2 x = −4, y = Carefully review your answers on this progress test and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to the online test submission page in the presence of your proctor. The University of Nebraska is an equal opportunity educator and employer. ©2019, The Board of Regents of the University of Nebraska. All rights reserved. Precalculus 2: Trigonometry Summary of Formulas Functions of the sum and difference of two angles: cos (A – B) = cos A cos B + sin A sin B cos (A + B) = cos A cos B – sin A sin B sin (A + B) = sin A cos B + cos A sin B sin (A – B) = sin A cos B – cos A sin B tan A + tan B tan (A + B) = 1 – tan A tan B tan A – tan B tan (A – B) = 1 + tan A tan B Functions of twice an angle (double-angle formulas): cos 2A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1 sin 2A = 2 sin A cos A tan 2A = 2 tan A 1 – tan2 A Functions of half an angle (half-angle formulas): Tables MTHH 044 Product formulas: 2 sin A cos B = sin (A + B) + sin (A – B) 2 cos A sin B = sin (A + B) – sin (A – B) 2 cos A cos B = cos (A + B) + cos (A – B) 2 sin A sin B = cos (A – B) – cos (A + B) Sum formulas: Tables Included in this section are three sets of tables. The first is the Table of Trigonometric Functions for angles written in degrees. The second is the Table of Trigonometric Functions for angles written in radians. The third table is a table of Logarithmic Functions. Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Tables MTHH 044 Table 3 - Logarithms of Numbers Tables MTHH 044 Tables MTHH 044
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