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Trigonometry

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Trigonometry

MathematicsK-12 Education
Tác giả
CK-12 Foundation
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LibreTexts
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LibreTexts
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CK-12
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EN
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Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 153 mục
  1. 01: Right Triangles and the Pythagorean Theorem
  2. 1.01: Pythagorean Theorem
  3. 1.02: Converse of the Pythagorean Theorem
  4. 1.03: Pythagorean Triples
  5. 1.04: Applications Using the Pythagorean Theorem
  6. 1.05: The Pythagorean Theorem for Area and Perimeter
  7. 1.06: Distance Formula and the Pythagorean Theorem
  8. 1.07: Pythagorean Theorem to Classify Triangles
  9. 1.08: Special Right Triangles and Ratios
  10. 1.09: 30-60-90 Right Triangles
  11. 1.10: 45-45-90 Right Triangles
  12. 02: Trigonometric Ratios
  13. 2.01: Trig Functions
  14. 2.1.01: Right Triangle Trigonometry
  15. 2.1.02: Calculator Trig Functions
  16. 2.1.03: SIN
  17. 2.1.04: COS
  18. 2.1.05: Sine and Cosine of Complementary Angles
  19. 2.1.06: TAN
  20. 2.1.07: SEC CSC COT
  21. 2.02: Solving Triangles
  22. 2.2.01: The Pythagorean Theorem and Trigonometry
  23. 2.2.02: Trig Function Applications
  24. 2.2.03: Right Triangles and Bearings
  25. 2.2.04: Solve Right Triangles
  26. 2.2.05: Applications of Inverse Trigonometric Functions
  27. 2.2.06: Inverse Trig Functions using Algebra
  28. 2.2.07: Angles of Elevation and Depression
  29. 2.03: Trig in the Unit Circle
  30. 2.3.01: Trigonometry and the Unit Circle
  31. 2.3.02: Measuring Rotation
  32. 2.3.03: Angles of Rotation in Standard Positions
  33. 2.3.04: Coterminal Angles
  34. 2.3.05: Signs of Trigonometric Functions
  35. 2.3.06: Trigonometric Functions and Angles of Rotation
  36. 2.3.07: Reference Angles and Angles in the Unit Circle
  37. 2.3.08: Trigonometric Functions of Negative Angles
  38. 2.3.09: Trigonometric Functions of Angles Greater than 360 Degrees
  39. 2.3.10: Exact Values for Inverse Sine Cosine and Tangent
  40. 2.04: Inverse Trigonometric Functions
  41. 2.4.01: Inverse Trig Functions
  42. 2.4.02: Inverses by Mapping
  43. 2.4.03: Composition of Trig Functions and Their Inverses
  44. 2.4.04: Definition of Inverse Reciprocal Trig Functions
  45. 2.4.05: Composition of Inverse Reciprocal Trig Functions
  46. 2.4.06: Trig Functions as Algebra Expressions
  47. 2.05: Radians
  48. 2.5.01: Radian Measure
  49. 2.5.02: Conversion between Degrees and Radians
  50. 2.5.03: Trig Functions and Radians with Technology
  51. 2.5.04: Rotations in Radians
  52. 2.5.05: Angular Velocity
  53. 2.5.06: Length of an Arc
  54. 2.5.07: Area of a Sector
  55. 2.5.08: Length of a Chord
  56. 2.06: Sine and Cosine Graphs
  57. 2.6.01: Sine Graph and Cosine Graph
  58. 2.6.02: Translating Sine and Cosine Functions
  59. 2.6.03: Vertical Translations
  60. 2.6.04: Horizontal Translations or Phase Shifts
  61. 2.6.05: Amplitude Period and Frequency
  62. 2.6.06: Amplitude
  63. 2.6.07: Period and Frequency
  64. 2.6.08: Trigonometric Identities and Equations
  65. 2.6.09: General Sinusoidal Graphs
  66. 2.07: Six Trig Function Graphs
  67. 2.7.01: Graphing Tangent Cotangent Secant and Cosecant
  68. 2.7.02: Tangent Graphs
  69. 2.7.03: Tangent and Cotangent Graphs
  70. 2.7.04: Sine and Cosecant Graphs
  71. 2.7.05: Cosine and Secant Graphs
  72. 2.7.06: Graph Inverse Trigonometric Functions
  73. 03: Trigonometric Identities
  74. 3.01: Trig Identities
  75. 3.1.01: Fundamental Trigonometric Identities
  76. 3.1.02: Quotient Identities
  77. 3.1.03: Reciprocal Identities
  78. 3.1.04: Pythagorean Identities
  79. 3.1.05: Even and Odd Identities
  80. 3.1.06: Cofunction Identities
  81. 3.02: Basic Trig Identity Applications
  82. 3.2.01: Trig Identities to Find Exact Trigonometric Values
  83. 3.2.02: Simplifying Trigonometric Expressions
  84. 3.2.03: Proofs of Trigonometric Identities
  85. 3.2.04: Simpler Form of Trigonometric Equations
  86. 3.2.05: Solving Trigonometric Equations
  87. 3.2.06: Solving Trigonometric Equations Using Basic Algebra
  88. 3.2.07: Trigonometric Equations Using the Quadratic Formula
  89. 3.2.08: Trigonometric Equations Using Factoring
  90. 3.03: Sum and Difference Identities
  91. 3.3.01: Sum and Difference Formulas
  92. 3.3.02: Simplifying Trigonometric Expressions using Sum and Difference Formulas
  93. 3.3.03: Sine Sum and Difference Formulas
  94. 3.3.04: Cosine Sum and Difference Formulas
  95. 3.3.05: Tangent Sum and Difference Formulas
  96. 3.3.06: Solving Trigonometric Equations using Sum and Difference Formulas
  97. 3.3.07: Finding Exact Trigonometric Values Using Sum and Difference Formulas
  98. 3.3.08: Applications of Sum and Difference Formulas
  99. 3.04: Double and Half Angle Identities
  100. 3.4.01: Double and Half Angle Formulas
  101. 3.4.02: Double Angle Identities
  102. 3.4.03: Simplifying Trigonometric Expressions with Double-Angle Identities
  103. 3.4.04: Solving Equations with Double-Angle Identities
  104. 3.4.05: Half Angle Formulas
  105. 3.4.06: Trigonometric Equations Using Half Angle Formulas
  106. 3.05: Sum to Product and Triple Angle Formulas
  107. 3.5.01: Sum to Product Formulas for Sine and Cosine
  108. 3.5.02: Product to Sum Formulas for Sine and Cosine
  109. 3.5.03: Triple-Angle Formulas and Linear Combinations
  110. 04: Non-Right Triangle Trigonometry
  111. 4.01: Law of Sines and Law of Cosines
  112. 4.1.01: Laws of Sines and Cosines
  113. 4.1.02: Law of Sines
  114. 4.1.03: Angle-Angle-Side Triangles
  115. 4.1.04: Angle-Side-Angle Triangles
  116. 4.1.05: Side-Side-Angle- The Ambiguous Case
  117. 4.1.06: Law of Cosines
  118. 4.1.07: Trigonometry Word Problems
  119. 4.1.08: Determination of Unknown Angles Using Law of Cosines
  120. 4.1.09: Identify Accurate Drawings of Triangles
  121. 4.1.10: Applications of the Law of Cosines
  122. 4.02: Area of Non-Right Triangles
  123. 4.2.01: Area Formula for Non-Right Triangles
  124. 4.2.02: Introduction to the Triangle Area Formula
  125. 4.2.03: Determination of Unknown Triangle Measures Given Area
  126. 4.2.04: Heron's Formula
  127. 4.2.05: General Solutions of Triangles
  128. 05: Polar System and Complex Numbers
  129. 5.01: The Polar Coordinate System
  130. 5.1.01: Plots of Polar Coordinates
  131. 5.1.02: Distance Between Two Polar Coordinates
  132. 5.1.03: Graph Polar Equations
  133. 5.1.04: Transformations of Polar Graphs
  134. 5.1.05: Special Polar Equations and Graphs
  135. 5.02: Polar Curves and Rectangular Conversions
  136. 5.2.01: Polar and Rectangular Conversions
  137. 5.2.02: Rectangular to Polar Conversions
  138. 5.2.03: Rectangular to Polar Form for Equations
  139. 5.2.04: Intersections of Polar Curves
  140. 5.2.05: Equivalent Polar Curves
  141. 5.2.06: Systems of Polar Equations
  142. 5.03: Complex Numbers
  143. 5.3.01: Imaginary Numbers
  144. 5.3.02: The Complex Numbers
  145. 5.3.03: Quadratic Formula and Complex Sums
  146. 5.3.04: Products and Quotients of Complex Numbers
  147. 5.3.05: Product and Quotient Theorems
  148. 5.3.06: Trigonometric Form of Complex Numbers
  149. 5.3.07: Equations Using DeMoivre's Theorem
  150. 5.3.08: Geometry of Complex Roots
  151. 5.3.09: Polar Form of a Complex Number
  152. 5.3.10: DeMoivre's Theorem and nth Roots
  153. 5.3.11: DeMoivre's Theorem