College Trigonometry, 2011a

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848 Foundations of <strong>Trigonometry</strong> (a) Clearly △AOB and △BCD are right triangles because the line through O and A and the line through C and D are perpendicular to the x-axis. Use the distance formula to show that △BAD is also a right triangle (with ∠BAD being the right angle) by showing that the sides of the triangle satisfy the Pythagorean Theorem. (b) Use △AOB to show that α =arctan(1) (c) Use △BAD to show that β =arctan(2) (d) Use △BCD to show that γ =arctan(3) (e) Use the fact that O, B and C all lie on the x-axis to conclude that α + β + γ = π. Thus arctan(1) + arctan(2) + arctan(3) = π.
10.6 The Inverse Trigonometric Functions 849 10.6.6 Answers ( 1. arcsin (−1) = − π √ ) ( 3 2. arcsin − = − π √ ) 2 3. arcsin − = − π 2 2 3 2 4 ( 4. arcsin − 1 ) = − π ( 1 5. arcsin (0) = 0 6. arcsin = 2 6 2) π 6 (√ ) (√ ) 2 7. arcsin = π 3 8. arcsin = π 9. arcsin (1) = π 2 4 2 3 2 ( √ ) ( 3 10. arccos (−1) = π 11. arccos − = 5π √ ) 2 12. arccos − = 3π 2 6 2 4 ( 13. arccos − 1 ) = 2π 2 3 (√ ) 2 16. arccos = π 2 4 14. arccos (0) = π 2 (√ ) 3 17. arccos = π 2 6 19. arctan ( − √ 3 ) = − π 20. arctan (−1) = − π 3 4 (√ ) 3 22. arctan (0) = 0 23. arctan = π 3 6 ( 1 15. arccos = 2) π 3 18. arccos (1) = 0 ( √ ) 3 21. arctan − = − π 3 6 24. arctan (1) = π 4 25. arctan (√ 3 ) = π 3 ( √ ) 3 28. arccot − = 2π 3 3 26. arccot ( − √ 3 ) = 5π 6 29. arccot (0) = π 2 27. arccot (−1) = 3π 4 (√ ) 3 30. arccot = π 3 3 31. arccot (1) = π 4 32. arccot (√ 3 ) = π 6 33. arcsec (2) = π 3 34. arccsc (2) = π 6 ( 2 √ ) 3 37. arcsec = π 3 6 35. arcsec (√ 2 ) = π 4 ( 2 √ ) 3 38. arccsc = π 3 3 36. arccsc (√ 2 ) = π 4 39. arcsec (1) = 0 40. arccsc (1) = π 2 41. arcsec (−2) = 4π 3 42. arcsec ( − √ 2 ) = 5π 4
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College Trigonometry Version ⌊π
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Table of Contents vii 10 Foundation
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 10 Foundations of Trigonome
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10.1 Angles and their Measure 695 k
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10.1 Angles and their Measure 697 2
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10.1 Angles and their Measure 701 T
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10.1 Angles and their Measure 703 y
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10.1 Angles and their Measure 705 y
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10.1 Angles and their Measure 707 h
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10.1 Angles and their Measure 711 I
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10.2 The Unit Circle: Cosine and Si
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30 ◦ 1 10.2 The Unit Circle: Cosi
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10.3 The Six Circular Functions and
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10.4 Trigonometric Identities 771 f
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10.4 Trigonometric Identities 773 2
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10.4 Trigonometric Identities 779 T
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10.4 Trigonometric Identities 781 R
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10.4 Trigonometric Identities 785 I
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10.5 Graphs of the Trigonometric Fu
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11.2 The Law of Sines 899 a angle-s
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11.2 The Law of Sines 901 determine
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11.2 The Law of Sines 903 Let x den
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11.2 The Law of Sines 905 24. Along
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11.2 The Law of Sines 907 33. The a
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11.2 The Law of Sines 909 25. (a)
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11.3 The Law of Cosines 911 of B ar
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11.3 The Law of Cosines 913 the pre
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11.3 The Law of Cosines 915 A 2 = =
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11.3 The Law of Cosines 917 22. A n
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11.4 Polar Coordinates 919 11.4 Pol
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11.4 Polar Coordinates 921 The poin
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11.4 Polar Coordinates 923 4. We mo
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11.4 Polar Coordinates 925 Solution
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11.4 Polar Coordinates 927 Solution
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11.4 Polar Coordinates 929 algebrai
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11.4 Polar Coordinates 931 45. ( )
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11.4 Polar Coordinates 933 5. ( 12,
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11.4 Polar Coordinates 935 13. (
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11.4 Polar Coordinates 937 73. r =7
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11.5 Graphs of Polar Equations 939
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11.6 Hooked on Conics Again 973 11.
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11.6 Hooked on Conics Again 975 Exa
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11.6 Hooked on Conics Again 977 The
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11.6 Hooked on Conics Again 979 We
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11.6 Hooked on Conics Again 983 The
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11.6 Hooked on Conics Again 985 In
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11.6 Hooked on Conics Again 989 2 9
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11.7 Polar Form of Complex Numbers
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11.8 Vectors 1013 Q ′ (1, 7) up 4
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11.8 Vectors 1015 ⃗v + ⃗w = 〈
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11.8 Vectors 1017 ⃗v − ⃗w =
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11.8 Vectors 1019 The remaining pro
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11.8 Vectors 1021 ‖k⃗v‖ = ‖
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11.8 Vectors 1023 at the origin, th
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11.8 Vectors 1025 Geometrically, th
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11.8 Vectors 1027 11.8.1 Exercises
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11.8 Vectors 1029 44. ⃗v = 〈−
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11.8 Vectors 1031 11.8.2 Answers 1.
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11.8 Vectors 1033 47. ‖⃗v‖ =2
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11.9 The Dot Product and Projection
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11.10 Parametric Equations 1049 obj
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11.10 Parametric Equations 1051 2.
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11.10 Parametric Equations 1053 Now
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11.10 Parametric Equations 1057 Our
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11.10 Parametric Equations 1061 Sup
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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Index 1073 reflective property, 523
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Index 1075 matrix, multiplicative,
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Index 1077 midpoint definition of,
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Index 1079 instantaneous, 161, 472
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Index 1081 inconsistent, 553 indepe
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College Trigonometry, 2011a

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