SECTION 7.4 Trigonometric Identities Skill Building In Problems 11-20, simplify each trigonometric expression by following the indicated direction. \I1. Rewrite in terms of sine and cosine functions: he numerator and \ 13. Multiply 15. Rewrite as a single quotient: MIS + ha 40 12. Rewrite in terms of sine and cosine functions: tan 0. csc 6. cot 0 sec 0. 1 + sin 0 by 1 + sin 0 cos 0 sin 0 14. Multiply sin 0 cos 0 1+ cos 0 by 1. cos e 16. Rewrite as a single quotient: sin 0 + cos 0 cos e - sin 0 1. 1- cos v sin 0 %3D cos 0 1. cos 6 (sin e + cos 0) (sin 0+ cos 0) 1 + cos v 1. 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - se sin e cos 0 3 sin? 0 + 4 sin e + 1 sin e + 2 sin 0 + 1 18. Multiply and simplify: tan 0 19. Factor and simplify: cos 0 - 1 20. Factor and simplify: cos e cos e In Problems 21-100, establish each identity. = cot 0 22. sec 0- sin 0 = tan 0 21. csc 0· cos e 23. 1 + tan (-0) sec? e establish ideni 24. 1+ cot (-0) = csc? e 25. cos 0 ( tan 6 + cot 0) = csc 0 26. sin 0 (cot 0 + tan 0) = sec 0 27. tan u cot u - cos u = sin? u 28. sin u csc u - cos u sin' u 29. (sec 0 - 1) (sec 0 + 1) = tan² e %3D 30. (csc 0 – 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 0) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) 33. cos 0 (1 + tan? 0) = 1 34. (1 - cos 6) (1 + cot? e) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos containing the m 36. tan 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec² 0 = tan 0 + tan? e 38. csc* 0 - csc2 0 = cot e + cot? cotient. Cos u sin u 39. sec u - tan u = 1 + sin u 40. csc u - cot u = 41. 3 sin e + 4 cos 0 = 3 + cos? E 1 + cos u nd cosine funci cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec e 43. 1 = sin 0 - cos 0 44. 1 - 1 + sin 0 e of the expresin le. 1 - sin v 1 + sin v 1 + tan v 45. cot v + 1 csc v - 1 46. sin sec 0 47. csc e 2 tan 0 tan v cot v - csc v + 1 cos 0 csc e - 1 48. cot 0 1 + sin 0 49. csc 0 + 1 cos 0 + 1 50. cos 0 cot e 1 + sec 0 csc 0 + 1 sin 6 csc 0 - 1 1 sec 0 1 - sin v cos v COS V 1 + sin v sin 0 1 \51. 52. = 2 sec v 53. sin 0 - cos 0 2 sec v cos v 1 - sin v 1 sin v Cs v 1 - cot 0 listed in red sin 0 : - sin 0 = (sec 0- tan 0)2 1- cos 0 56. 1 + cos 0 54. 1 - = cos 0 (csc 0 - cot 0) 1 + cos 0 1 + sin 9 cos 0 sin 0 cot 0 tan 0 57. 1 - tan 0 sin 0+ cos 58. 1 - tan 0 = 1 + tan 0 + cot 0 %3D 1 - cot 0 1 - cot 0 Ços e sin 0 cos 0 tan 0 tan 0 + sec 0 - 1 61 ton 0 denomincal the denominator
SECTION 7.4 Trigonometric Identities Skill Building In Problems 11-20, simplify each trigonometric expression by following the indicated direction. \I1. Rewrite in terms of sine and cosine functions: he numerator and \ 13. Multiply 15. Rewrite as a single quotient: MIS + ha 40 12. Rewrite in terms of sine and cosine functions: tan 0. csc 6. cot 0 sec 0. 1 + sin 0 by 1 + sin 0 cos 0 sin 0 14. Multiply sin 0 cos 0 1+ cos 0 by 1. cos e 16. Rewrite as a single quotient: sin 0 + cos 0 cos e - sin 0 1. 1- cos v sin 0 %3D cos 0 1. cos 6 (sin e + cos 0) (sin 0+ cos 0) 1 + cos v 1. 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - se sin e cos 0 3 sin? 0 + 4 sin e + 1 sin e + 2 sin 0 + 1 18. Multiply and simplify: tan 0 19. Factor and simplify: cos 0 - 1 20. Factor and simplify: cos e cos e In Problems 21-100, establish each identity. = cot 0 22. sec 0- sin 0 = tan 0 21. csc 0· cos e 23. 1 + tan (-0) sec? e establish ideni 24. 1+ cot (-0) = csc? e 25. cos 0 ( tan 6 + cot 0) = csc 0 26. sin 0 (cot 0 + tan 0) = sec 0 27. tan u cot u - cos u = sin? u 28. sin u csc u - cos u sin' u 29. (sec 0 - 1) (sec 0 + 1) = tan² e %3D 30. (csc 0 – 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 0) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) 33. cos 0 (1 + tan? 0) = 1 34. (1 - cos 6) (1 + cot? e) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos containing the m 36. tan 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec² 0 = tan 0 + tan? e 38. csc* 0 - csc2 0 = cot e + cot? cotient. Cos u sin u 39. sec u - tan u = 1 + sin u 40. csc u - cot u = 41. 3 sin e + 4 cos 0 = 3 + cos? E 1 + cos u nd cosine funci cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec e 43. 1 = sin 0 - cos 0 44. 1 - 1 + sin 0 e of the expresin le. 1 - sin v 1 + sin v 1 + tan v 45. cot v + 1 csc v - 1 46. sin sec 0 47. csc e 2 tan 0 tan v cot v - csc v + 1 cos 0 csc e - 1 48. cot 0 1 + sin 0 49. csc 0 + 1 cos 0 + 1 50. cos 0 cot e 1 + sec 0 csc 0 + 1 sin 6 csc 0 - 1 1 sec 0 1 - sin v cos v COS V 1 + sin v sin 0 1 \51. 52. = 2 sec v 53. sin 0 - cos 0 2 sec v cos v 1 - sin v 1 sin v Cs v 1 - cot 0 listed in red sin 0 : - sin 0 = (sec 0- tan 0)2 1- cos 0 56. 1 + cos 0 54. 1 - = cos 0 (csc 0 - cot 0) 1 + cos 0 1 + sin 9 cos 0 sin 0 cot 0 tan 0 57. 1 - tan 0 sin 0+ cos 58. 1 - tan 0 = 1 + tan 0 + cot 0 %3D 1 - cot 0 1 - cot 0 Ços e sin 0 cos 0 tan 0 tan 0 + sec 0 - 1 61 ton 0 denomincal the denominator
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 59E
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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