546 CHAPTER 5 Trigonometric Functions NOTE Example 11 can also be worked by sketching u in standard position in quadrant III, finding r to be 5, and then using the definitions of sin u and cos u in terms of x, y, and r. See Figure 26. When using this method, be sure to choose the correct signs for x and y as determined by the quadrant in which the terminal side of u lies. This is analogous to choosing the correct signs after applying the Pythagorean identities. x y 0 x = –3 y = –4 r = 5 (–3, –4) u 3 –4 –3 3 –4 5 Figure 26 5.2 Exercises CONCEPT PREVIEW The terminal side of an angle u in standard position passes through the point 1-3, -32. Use the figure to find the following values. Rationalize denominators when applicable. 1. r 2. sin u 3. cos u 4. tan u x y 0 r –3 –3 (–3, –3) u CONCEPT PREVIEW Determine whether each statement is possible or impossible. 5. sin u = 1 2 , csc u = 2 6. tan u = 2, cot u = -2 7. sin u 70, csc u 60 8. cos u = 1.5 9. cot u = -1.5 10. sin2 u + cos2 u = 2 Sketch an angle u in standard position such that u has the least positive measure, and the given point is on the terminal side of u. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. 11. 15, -122 12. 1-12, -52 13. 13, 42 14. 1-4, -32 15. 1-8, 152 16. 115, -82 17. 1-7, -242 18. 1-24, -72 19. 10, 22 20. 10, 52 21. 1-4, 02 22. 1-5, 02 23. A1, 23 B 24. A -1, 23 B 25. A -223, -2B 26. A -223, 2B Concept Check Suppose that the point 1x, y2 is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = 2x2 + y2. (Hint: Drawing a sketch may help.) 27. II, x r 28. III, y r 29. IV, y x 30. IV, x y 31. II, y r 32. III, x r 33. IV, x r 34. IV, y r 35. II, x y 36. II, y x 37. III, y x 38. III, x y 39. III, r x 40. III, r y 41. I, x y 42. I, y x
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