University:
Williams College
Course:
MATH 102 | Foundations in Quantitative Skills
Academic year:

2021
Views:

454

Pages:

6
Author:

Rashad Montoya

Quiz Review Name:_______________________________________ Hour:______ Plot the point that has the given polar coordinates. Label each point! 1. (3, 3. (1, 5𝜋 ) 4 2. (−4, 7𝜋 ) 2 4. (3, − 5. (−2, 5𝜋 ) 6 2𝜋 ) 3 𝜋 2 2𝜋 3 13𝜋 ) 6 𝜋 3 5𝜋 6 𝜋 6 6. (−1, −7𝜋) 𝜋 7. (−3, − 9. (4, 5𝜋 ) 6 4𝜋 ) 3 𝜋 8. (−2, − 3 ) 10. (−1, 11. (−2, 6𝜋) 0 12. 7𝜋 6 3𝜋 ) 4 11𝜋 6 4𝜋 3 7𝜋 (3, − 6 ) 5𝜋 3 3𝜋 2 Determine which point in the figure, P, Q, R, or S has the given polar coordinate. 𝜋 2 𝜋 13. (2, − 6 ) 14. (2, 2𝜋 3 7𝜋 ) 6 15. 𝜋 (−2, 6 ) 16. 5𝜋 (−2, − 6 ) 17. (−2, − 11𝜋 ) 6 5𝜋 6 𝜋 6 Q 11𝜋 (2, ) 6 P 𝜋 0 𝜋 18. (2, 6 ) 19. 𝜋 3 S R 7𝜋 6 11𝜋 6 4𝜋 3 5𝜋 3 3𝜋 2 Find three other polar coordinate representations of the point where −𝟐𝝅 < 𝜽 < 𝟐𝝅. 20. (−5, 5𝜋 ) 6 21. (8, − 2𝜋 ) 3 22. (10, 23. (−3, 7𝜋 ) 4 24. (2, − 3 ) 5𝜋 ) 2 𝜋 25. (−1, 7𝜋 ) 6 Find the corresponding rectangular coordinates for the given polar coordinate. 26. (4, 2𝜋 ) 3 29. (−4, 13𝜋 ) 3 27. (3, − 7𝜋 ) 6 30. (3, 8𝜋) 28. (6, 17𝜋 ) 2 31. (6.42, 3.59) Find the corresponding polar coordinates for the given rectangular coordinate where 𝟎 ≤ 𝜽 < 𝟐𝝅. 32. (−5, −5) 33. (−√3, 1) 34. (4, −4√3) 35. (0, 8) 36. (−1, 0) 37. (−12, 5) Convert the rectangular equation to polar form. 38. 𝑥 = 5 39. 4𝑦 + 𝑥 − 2 = 0 40. 𝑥 2 + 𝑦 2 + 4𝑦 = 0 41. 𝑥 2 + 𝑦 2 + 8𝑥 = 0 Convert the polar equation to rectangular form. 42. 𝜃 = 5𝜋 3 43. 𝑟 = 3 sin 𝜃 44. 𝑟 = 4 Convert the polar equation to rectangular form. 45. 𝑟 = 3 sec 𝜃 6 46. 𝑟 = 1−2 cos 𝜃 Graph the polar equation. 48. 𝑟 = 3 sin 𝜃 49. 𝑟 = −4 cos 𝜃 Name: Name: 50. 𝑟 = 2 − 2 sin 𝜃 51. 𝑟 = 1 + 3 cos 𝜃 Name: Name: 3 47. 𝑟 = 1−sin 𝜃 52. 𝑟 = 2 cos 3𝜃 53. 𝑟 = 3sin 2𝜃 Name: Name: 54. 𝑟 2 = 9 sin 2𝜃 55. 𝑟 2 = 4 cos 2𝜃 Name: Name: Match the equation with its graph. 56. 𝑟 = −2 sin 𝜃 57. 𝑟 = 3 cos 5𝜃 58. 𝑟 = 2 + 3 cos 𝜃 59. 𝑟 2 = 6 sin 2𝜃 60. 𝑟 = 3 sin 6𝜃 61. 𝑟 = −2 − 2 cos 𝜃 62. 𝑟 2 = 6 cos 2𝜃 63. 𝑟 = 3 cos 𝜃 A. B. C. D. E. F. G. H. Answers: 1-12. See worked-out solutions 20. (−5, − 7𝜋 11𝜋 𝜋 ) (5, 6 ) (5, − 6 ) 6 23. (−3, − 4 ) (3, 𝜋 3𝜋 5𝜋 ) (3, − 4 ) 4 26. (−2, 2√3) 27. (− 32. (5√2, 5𝜋 ) 4 33. (2, 2 39. 𝑟 = 4 sin 𝜃+cos 𝜃 44. 𝑥 2 + 𝑦 2 = 16 21. (8, 24. (2, 3√3 3 , ) 2 2 5𝜋 ) 6 13. S 34. (8, 15. R 16. P 4𝜋 𝜋 5𝜋 ) (−8, 3 ) (−8, − 3 ) 3 5𝜋 2𝜋 4𝜋 ) (−2, 3 ) (−2, − 3 ) 3 28. (0, 6) 5𝜋 ) 3 40. 𝑟 = −4 sin 𝜃 45. 𝑥 = 3 14. R 29. (−2, −2√3) 𝜋 35. (8, 2 ) 48-55. See worked-out solutions 56. D 57. G 𝜋 25. (−1, − 30. (3, 0) 58. A 19. S 3𝜋 3𝜋 ) (−10, 2 ) 2 5𝜋 𝜋 11𝜋 ) (1, 6 ) (1, − 6 ) 6 31. (−5.79, −2.78) 37. (13, 2.75) 42. 𝑦 = −√3𝑥 46. −3𝑥 2 + 𝑦 2 − 24𝑥 − 36 = 0 18. P 22. (10, 2 ) (10, − 36. (1, 𝜋) 41. 𝑟 = −8 cos 𝜃 17. R 38. 𝑟 = 5 sec 𝜃 43. 𝑥 2 + 𝑦 2 − 3𝑦 = 0 47. 𝑥 2 − 6𝑦 − 9 = 0 59. F 60. C 61. H 62. B 63. E

Math Polar Coordinates Quiz Review Answers

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock