Complete the worksheet, show work for each problem. Let me know if something is unclear.

Prove each trigonometric identity. 1. sin 0sec 0 = tan 0 2. cot(-0) = -cote 3. cos20 (sec20 - 1) = sin20 Rewrite each expression in terms of cos 0, and simplify. 4. csc Otan 0 5. (1 + sec 0)(1 - sin 0) 6. sin20 + cos20 + tan?0 7. Physics Use the equation mg sin 0 = umg cos @ to determine the angle at which a H = 0.94. glass-top table can be tilted before a glass plate on the table begins to slide. Assume PRACTICE AND PROBLEM SOLVING Prove each trigonometric identity. 8. sec @cot 0 = csco 9. sino - cose =1 - cote sin 0 10. tan Osin 0 = sec0 - cos 0 11. sec2 0 (1- cos20) = tan20 Rewrite each expression in terms of sin 0, and simplify. COEFFICIENT 12. cos e 13. tane OF FRICTION 1 + sin 0 M=0.9 cote 14. cos @ cote + sine 15. sec2 0 - 1 1 + tan e 16. Physics Use the equation mgsin 0 = umg cos 0 to 1 HOUR determine the steepest slope of the street shown on PARKING which a car with rubber tires can park without sliding. Multi-Step Rewrite each expression in terms of a single trigonometric function. 17. tan 0cote 18. sin Ocot Otan 0 19. cose + sin 0 tan 0 20. sin Acsc 0 - cos2 0 21. cos2 0sec ecsce 22. cose( tan20 + 1) 23. csce(1 - cos2 0) 24. csc ecos Otan @ 25. sin 0 1 - cose 26. sin20 27. tan e 28. cos e 1 - cos20 sin 0 sec e sin 0 cot e 29. tan 0 (tane + cote) 30. sin20 + cos20 + cot20 31. sin20 sec0 csco Verify each identity. 32. cose -1 = sec0 - sec2 0 33. sin20(csc20 -1) = cos20 34. tand + cot0 = sec @ csco cos 0 35. cos 0 = sec 0 36. 1 - cos2 0 = sin @ cos 0 37. _csc20 = cot20 1 - sin 0 tan 0 1 + tan20 Prove each fundamental identity without using any of the other fundamental identities. (Hint: Use the trigonometric ratios with x, y, and r.) 38. tano = sino 39. cote = cose sin 0 40. 1 + cot20 = csc20 cos ! 1 42. sec 0 = 41. csc 0 = cos 0 43. 1 + tan20 = sec20 sin 8