848 CHAPTER 8 Applications of Trigonometry CONCEPT PREVIEW For each point given in polar coordinates, state the quadrant in which the point lies if it is graphed in a rectangular coordinate system. 5. 15, 135°2 6. 12, 60°2 7. 16, -30°2 8. 14.6, 213°2 CONCEPT PREVIEW For each point given in polar coordinates, state the axis on which the point lies if it is graphed in a rectangular coordinate system. Also state whether it is on the positive portion or the negative portion of the axis. (For example, 15, 0°2 lies on the positive x-axis.) 9. 17, 360°2 10. 14, 180°2 11. 12, -90°2 12. 18, 450°2 For each pair of polar coordinates, (a) plot the point, (b) give two other pairs of polar coordinates for the point, and (c) give the rectangular coordinates for the point. See Examples 1 and 2(a). 13. 11, 45°2 14. 13, 120°2 15. 1-2, 135°2 16. 1-4, 30°2 17. 15, -60°2 18. 12, -45°2 19. 1-3, -210°2 20. 1-1, -120°2 21. a3, 5p 3 b 22. a4, 3p 2 b 23. a-2, p 3b 24. a-5, 5p 6 b For each pair of rectangular coordinates, (a) plot the point and (b) give two pairs of polar coordinates for the point, where 0° … u 6360°. See Example 2(b). 25. 11, -12 26. 11, 12 27. 10, 32 28. 10, -32 29. A 22, 22 B 30. A -22, 22 B 31. ¢ 23 2 , 3 2≤ 32. ¢- 23 2 , - 1 2≤ 33. 13, 02 34. 1-2, 02 35. ¢- 3 2 , - 323 2 ≤ 36. ¢ 1 2 , - 23 2 ≤ For each rectangular equation, give the equivalent polar equation and sketch its graph. See Example 3. 37. x - y = 4 38. x + y = -7 39. x2 + y2 = 16 40. x2 + y2 = 9 41. 2x + y = 5 42. 3x - 2y = 6 Concept Check Match each equation with its polar graph from choices A – D. 43. r = 3 44. r = cos 3u 45. r = cos 2u 46. r = 2 cos u +sin u A. 1808 08 908 2708 1 B. 2 1808 08 908 2708 C. 3 1808 08 908 2708 D. 1 1808 08 908 2708
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