Trigonometry worksheet for calculating sine, cosine, and tangent ratios for different angles.

Final Answer:
1. sin P° = 3/5, 7. cos Y° = 4/5, 13. sin X° = 4/5
2. cos P° = 4/5, 8. cos Y° = 3/5, 14. cos X° = 3/5
3. tan P° = 3/4, 9. tan Y° = 4/3, 15. tan X° = 4/3
4. sin Q° = 4/5, 10. sin D° = 5/13, 16. sin Y° = 3/5
5. cos Q° = 3/5, 11. cos D° = 12/13, 17. cos Y° = 4/5
6. tan Q° = 4/3, 12. tan D° = 5/12, 18. tan Y° = 3/4
19. sin 30° = 0.5, 20. cos 60° = 0.5, 25. tan 45° = 1
21. sin 60° = √3/2 ≈ 0.866, 22. cos 45° = √2/2 ≈ 0.707, 26. tan 60° = √3 ≈ 1.732
23. sin 45° = √2/2 ≈ 0.707, 24. cos 30° = √3/2 ≈ 0.866, 27. tan 30° = √3/3 ≈ 0.577
28. sin 90° = 1, 29. cos 0° = 1, 30. tan 0° = 0
31. sin 0° = 0, 32. cos 90° = 0, 33. tan 90° is undefined
34. sin 180° = 0, 35. cos 180° = −1, 36. tan 180° = 0
37. sin 270° = −1, 38. cos 270° = 0, 39. tan 270° is undefined
40. sin 360° = 0, 41. cos 360° = 1, 42. tan 360° = 0

43. Because sine and cosine are ratios of sides (opposite/hypotenuse or adjacent/hypotenuse), and the hypotenuse is always the longest side, so those ratios can never be more than 1 or less than −1. Tangent is opposite/adjacent — those sides can be any length, so tangent can be any real number (including values >1 or <−1).