Introduction |
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xi | |
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Chapter 1 Angles and Their Measure |
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1 | (10) |
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Definitions and Terminology |
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1 | (3) |
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Complementary and Supplementary Angles |
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4 | (1) |
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Coterminal Angles and Reference Angles |
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4 | (3) |
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7 | (4) |
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Chapter 2 Concepts from Geometry |
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11 | (8) |
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The Sum of a Triangle's Angles and the Triangle Inequality |
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11 | (3) |
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14 | (5) |
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Chapter 3 Right Triangle Trigonometry |
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19 | (6) |
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Trigonometric Ratios of an Acute Angle in a Right Triangle |
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19 | (3) |
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Trigonometric Ratios of Special Acute Angles |
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22 | (3) |
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Chapter 4 General Right Triangles |
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25 | (6) |
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25 | (2) |
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Applications of Right Triangle Trigonometry |
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27 | (4) |
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Chapter 5 Oblique Triangles |
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31 | (18) |
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Law of Cosines (SAS or SSS) |
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31 | (4) |
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Law of Sines (AS A or A AS) |
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35 | (4) |
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Law of Sines Ambiguous Case (SSA) |
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39 | (2) |
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Solving General Triangles |
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41 | (5) |
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Area of a General Triangle Using Trigonometry |
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46 | (3) |
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Chapter 6 Trigonometric Functions of Any Angle |
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49 | (20) |
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Definitions of the Trigonometric Functions |
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49 | (4) |
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Trigonometric Functions of Complementary Angles |
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53 | (3) |
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56 | (3) |
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Trigonometric Functions of Quadrantal Angles |
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59 | (2) |
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Trigonometric Functions of Coterminal Angles |
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61 | (2) |
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Trigonometric Functions of Negative Angles |
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63 | (1) |
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Using Reference Angles to Find the Values of Trigonometric Functions |
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64 | (5) |
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Chapter 7 Trigonometric Identities |
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69 | (18) |
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Definition and Guidelines |
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69 | (2) |
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The Reciprocal and Ratio Identities |
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71 | (1) |
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The Pythagorean Identities |
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72 | (2) |
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Sum and Difference Formulas for the Sine Function |
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74 | (2) |
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Sum and Difference Formulas for the Cosine Function |
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76 | (2) |
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Sum and Difference Formulas for the Tangent Function |
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78 | (2) |
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80 | (1) |
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81 | (2) |
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83 | (2) |
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Sum-to-Product Identities |
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85 | (1) |
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Product-to-Sum Identities |
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86 | (1) |
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Chapter 8 Trigonometric Functions of Real Numbers |
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87 | (6) |
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Definitions and Basic Concepts of Trigonometric Functions of Real Numbers |
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87 | (2) |
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89 | (4) |
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Chapter 9 Graphs of the Sine Function |
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93 | (10) |
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93 | (2) |
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95 | (2) |
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The Graph of y = A sin Bx |
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97 | (3) |
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The Graph of y = A sin (Bx -- C) |
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100 | (3) |
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Chapter 10 The Graph of y = A sin (Bx -- C) + D |
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103 | (10) |
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Graphs of the Cosine Function |
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107 | (1) |
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107 | (2) |
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The Graph of y = A cos (Bx -- C) + D |
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109 | (4) |
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Chapter 11 Graphs of the Tangent Function |
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113 | (4) |
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113 | (1) |
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The Graph of y = A tan (Bx -- C) + D |
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114 | (3) |
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Chapter 12 Graphs of the Secant, Cosecant, and Cotangent Functions |
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117 | (8) |
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The Graph of y = A sec (Bx -- C) + D |
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117 | (2) |
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The Graph of y = A esc (Bx -- C) + D |
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119 | (2) |
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The Graph of y = A cot (Bx -- C) + D |
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121 | (4) |
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Chapter 13 Inverse Trigonometric Functions |
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125 | (10) |
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The Inverse Sine, Cosine, and Tangent Functions |
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125 | (5) |
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The Inverse Secant, Cosecant, and Cotangent Functions |
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130 | (5) |
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Chapter 14 Solving Trigonometric Equations |
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135 | (8) |
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Basic Concepts of Trigonometric Equations |
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135 | (4) |
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Solving for Exact Solutions to Trigonometric Equations |
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139 | (2) |
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Solving for Approximate Solutions to Trigonometric Equations |
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141 | (2) |
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Chapter 15 Trigonometric Form of a Complex Number |
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143 | (10) |
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Definition of the Trigonometric Form of a Complex Number |
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143 | (2) |
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The Product and Quotient of Trigonometric Forms of Complex Numbers |
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145 | (3) |
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148 | (1) |
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149 | (4) |
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Chapter 16 Polar Coordinates |
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153 | (1) |
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Basic Concepts of Polar Coordinates |
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153 | (2) |
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Converting Between Coordinate Systems |
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155 | (2) |
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Graphing Equations in Polar Form |
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157 | (1) |
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158 | (1) |
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APPENDIX A Calculator Instructions for Trigonometry Using the TI-84 Plus |
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159 | (10) |
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169 | (1) |
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Setting the Calculator to Degree or Radian Mode |
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170 | (1) |
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Overriding Radian or Degree Mode |
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170 | (1) |
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Evaluating Trigonometric Functions |
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170 | (3) |
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Determining Inverse Trigonometric Values |
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173 | (3) |
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176 | (3) |
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APPENDIX B Trigonometric Identities |
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179 | (2) |
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APPENDIX C The Complex Plane |
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181 | (2) |
Answer Key |
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183 | |