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Algebra and Trigonometry

Nguồn ngoài

Algebra and Trigonometry

Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.

AlgebraMathematics
Tác giả
Jay Abramson
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OpenStax
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LibreTexts
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CC BY
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EN
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Mục lục· 184 mục
  1. 01: Prerequisites
  2. 1.00: Prelude to Prerequisites
  3. 1.01: Real Numbers - Algebra Essentials
  4. 1.1E: Real Numbers - Algebra Essentials (Exercises)
  5. 1.02: Exponents and Scientific Notation
  6. 1.2E: Exponents and Scientific Notation (Exercises)
  7. 1.03: Radicals and Rational Expressions
  8. 1.3E: Radicals and Rational Expressions (Exercise)
  9. 1.04: Polynomials
  10. 1.4E: Polynomials (Exercises)
  11. 1.05: Factoring Polynomials
  12. 1.5E: Factoring Polynomials (Exercises)
  13. 1.06: Rational Expressions
  14. 1.6E: Rational Expressions (Exercises)
  15. 02: Equations and Inequalities
  16. 2.00: Prelude to Equations and Inequalities
  17. 2.01: The Rectangular Coordinate Systems and Graphs
  18. 2.1.00: The Rectangular Coordinate Systems and Graphs (Exercises)
  19. 2.02: Linear Equations in One Variable
  20. 2.2.00: Linear Equations in One Variable (Exercises)
  21. 2.03: Models and Applications
  22. 2.3.00: Models and Applications (Exercises)
  23. 2.04: Complex Numbers
  24. 2.4.00: Complex Numbers (Exercises)
  25. 2.05: Quadratic Equations
  26. 2.5.00: Quadratic Equations (Exercises)
  27. 2.06: Other Types of Equations
  28. 2.6.00: Other Types of Equations (Exercises)
  29. 2.07: Linear Inequalities and Absolute Value Inequalities
  30. 2.7.00: Linear Inequalities and Absolute Value Inequalities (Exercises)
  31. 03: Functions
  32. 3.00: Prelude to Functions
  33. 3.01: Functions and Function Notation
  34. 3.1E: Functions and Function Notation (Exercises)
  35. 3.02: Domain and Range
  36. 3.2E: Domain and Range (Exercises)
  37. 3.03: Rates of Change and Behavior of Graphs
  38. 3.3E: Rates of Change and Behavior of Graphs (Exercises)
  39. 3.04: Composition of Functions
  40. 3.4E: Composition of Functions (Exercises)
  41. 3.05: Transformation of Functions
  42. 3.5E: Transformation of Functions (Exercises)
  43. 3.06: Absolute Value Functions
  44. 3.6E: Absolute Value Functions (Exercises)
  45. 3.07: Inverse Functions
  46. 3.7E: Inverse Functions (Exercises)
  47. 04: Linear Functions
  48. 4.00: Introduction to Linear Functions
  49. 4.01: Linear Functions
  50. 4.1E: Linear Functions (Exercises)
  51. 4.02: Modeling with Linear Functions
  52. 4.2E: Modeling with Linear Functions (Exercises)
  53. 4.03: Fitting Linear Models to Data
  54. 4.3E: Fitting Linear Models to Data (Exercises)
  55. 05: Polynomial and Rational Functions
  56. 5.00: Prelude to Polynomial and Rational Functions
  57. 5.01: Quadratic Functions
  58. 5.1E: Quadratic Functions (Exercises)
  59. 5.02: Power Functions and Polynomial Functions
  60. 5.2E: Power Functions and Polynomial Functions (Exercises)
  61. 5.03: Graphs of Polynomial Functions
  62. 5.3E: Graphs of Polynomial Functions (Exercises)
  63. 5.04: Dividing Polynomials
  64. 5.4E: Dividing Polynomials (Exercises)
  65. 5.05: Zeros of Polynomial Functions
  66. 5.5E: Zeros of Polynomial Functions (Exercises)
  67. 5.06: Rational Functions
  68. 5.6E: Rational Functions (Exercises)
  69. 5.07: Inverses and Radical Functions
  70. 5.7E: Inverses and Radical Functions (Exercises)
  71. 5.08: Modeling Using Variation
  72. 5.8E: Modeling Using Variation (Exercises)
  73. 06: Exponential and Logarithmic Functions
  74. 6.00: Prelude to Exponential and Logarithmic Functions
  75. 6.01: Exponential Functions
  76. 6.1E: Exponential Functions (Exercises)
  77. 6.02: Graphs of Exponential Functions
  78. 6.2E: Graphs of Exponential Functions (Exercises)
  79. 6.03: Logarithmic Functions
  80. 6.3E: Logarithmic Functions (Exercises)
  81. 6.04: Graphs of Logarithmic Functions
  82. 6.4E: Graphs of Logarithmic Functions (Exercises)
  83. 6.05: Logarithmic Properties
  84. 6.5E: Logarithmic Properties (Exercises)
  85. 6.06: Exponential and Logarithmic Equations
  86. 6.6E: Exponential and Logarithmic Equations (Exercises)
  87. 6.07: Exponential and Logarithmic Models
  88. 6.7E: Exponential and Logarithmic Models (Exercises)
  89. 6.08: Fitting Exponential Models to Data
  90. 6.8E: Fitting Exponential Models to Data (Exercises)
  91. 07: The Unit Circle - Sine and Cosine Functions
  92. 7.00: Introduction to The Unit Circle- Sine and Cosine Functions
  93. 7.01: Angles
  94. 7.1E: Angles (Exercises)
  95. 7.02: Right Triangle Trigonometry
  96. 7.2E: Right Triangle Trigonometry (Exercises)
  97. 7.03: Unit Circle
  98. 7.3E: Unit Circle (Exercises)
  99. 7.04: The Other Trigonometric Functions
  100. 7.4E: The Other Trigonometric Functions (Exercises)
  101. 08: Periodic Functions
  102. 8.00: Introduction to Periodic Functions
  103. 8.01: Graphs of the Sine and Cosine Functions
  104. 8.1E: Graphs of the Sine and Cosine Functions (Exercises)
  105. 8.02: Graphs of the Other Trigonometric Functions
  106. 8.2E: Graphs of the Other Trigonometric Functions (Exercises)
  107. 8.03: Inverse Trigonometric Functions
  108. 8.3E: Inverse Trigonometric Functions (Exercises)
  109. 09: Trigonometric Identities and Equations
  110. 9.00: Prelude to Trigonometric Identities and Equations
  111. 9.01: Solving Trigonometric Equations with Identities
  112. 9.1E: Solving Trigonometric Equations with Identities (Exercises)
  113. 9.02: Sum and Difference Identities
  114. 9.2E: Sum and Difference Identities (Exercises)
  115. 9.03: Double-Angle Half-Angle and Reduction Formulas
  116. 9.3E: Double-Angle Half-Angle and Reduction Formulas (Exercises)
  117. 9.04: Sum-to-Product and Product-to-Sum Formulas
  118. 9.4E: Sum-to-Product and Product-to-Sum Formulas (Exercises)
  119. 9.05: Solving Trigonometric Equations
  120. 9.5E: Solving Trigonometric Equations (Exercises)
  121. 10: Further Applications of Trigonometry
  122. 10.00: Prelude to Further Applications of Trigonometry
  123. 10.01: Non-right Triangles - Law of Sines
  124. 10.1E: Non-right Triangles - Law of Sines (Exercises)
  125. 10.02: Non-right Triangles - Law of Cosines
  126. 10.2E: Non-right Triangles - Law of Cosines (Exercises)
  127. 10.03: Polar Coordinates
  128. 10.3E: Polar Coordinates (Exercises)
  129. 10.04: Polar Coordinates - Graphs
  130. 10.4E: Polar Coordinates - Graphs (Exercises)
  131. 10.05: Polar Form of Complex Numbers
  132. 10.5E: Polar Form of Complex Numbers (Exercises)
  133. 10.06: Parametric Equations
  134. 10.6E: Parametric Equations (Exercises)
  135. 10.07: Parametric Equations- Graphs
  136. 10.7E: Parametric Equations- Graphs (Exercises)
  137. 10.08: Vectors
  138. 10.8E: Vectors (Exercises)
  139. 11: Systems of Equations and Inequalities
  140. 11.00: Prelude to Systems of Equations and Inequalities
  141. 11.01: Systems of Linear Equations - Two Variables
  142. 11.1E: Systems of Linear Equations - Two Variables (Exercises)
  143. 11.02: Systems of Linear Equations with Three Variables
  144. 11.2E: Systems of Linear Equations with Three Variables (Exercises)
  145. 11.03: Systems of Nonlinear Equations and Inequalities - Two Variables
  146. 11.3E: Systems of Nonlinear Equations and Inequalities - Two Variables (Exercises)
  147. 11.04: Partial Fractions
  148. 11.4E: Partial Fractions (Exercises)
  149. 11.05: Matrices and Matrix Operations
  150. 11.5E: Matrices and Matrix Operations (Exercises)
  151. 11.06: Solving Systems with Gaussian Elimination
  152. 11.6E: Solving Systems with Gaussian Elimination (Exercises)
  153. 11.07: Solving Systems with Inverses
  154. 11.7E: Solving Systems with Inverses (Exercises)
  155. 11.08: Solving Systems with Cramer's Rule
  156. 11.8E: Solving Systems with Cramer's Rule (Exercises)
  157. 12: Analytic Geometry
  158. 12.00: Prelude to Analytic Geometry
  159. 12.01: The Ellipse
  160. 12.1E: The Ellipse (Exercises)
  161. 12.02: The Hyperbola
  162. 12.2E: The Hyperbola (Exercises)
  163. 12.03: The Parabola
  164. 12.3E: The Parabola (Exercises)
  165. 12.04: Rotation of Axes
  166. 12.4E: Rotation of Axes (Exercises)
  167. 12.05: Conic Sections in Polar Coordinates
  168. 12.5E: Conic Sections in Polar Coordinates (Exercises)
  169. 13: Sequences Probability and Counting Theory
  170. 13.00: Prelude to Sequences Probability and Counting Theory
  171. 13.01: Sequences and Their Notations
  172. 13.1E: Sequences and Their Notations (Exercises)
  173. 13.02: Arithmetic Sequences
  174. 13.2E: Arithmetic Sequences (Exercises)
  175. 13.03: Geometric Sequences
  176. 13.3E: Geometric Sequences (Exercises)
  177. 13.04: Series and Their Notations
  178. 13.4E: Series and Their Notations (Exercises)
  179. 13.05: Counting Principles
  180. 13.5E: Counting Principles (Exercises)
  181. 13.06: Binomial Theorem
  182. 13.6E: Binomial Theorem (Exercises)
  183. 13.07: Probability
  184. 13.7E: Probability (Exercises)