Algebra and Trigonometry

by Jay Abramson

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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.

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Publisher
OpenStax
Subjects
Mathematics, Algebra
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Prerequisites
  7. 1.0: Prelude to Prerequisites
  8. 1.1: Real Numbers - Algebra Essentials
  9. 1.1E: Real Numbers - Algebra Essentials (Exercises)
  10. 1.2: Exponents and Scientific Notation
  11. 1.2E: Exponents and Scientific Notation (Exercises)
  12. 1.3: Radicals and Rational Expressions
  13. 1.3E: Radicals and Rational Expressions (Exercise)
  14. 1.4: Polynomials
  15. 1.4E: Polynomials (Exercises)
  16. 1.5: Factoring Polynomials
  17. 1.5E: Factoring Polynomials (Exercises)
  18. 1.6: Rational Expressions
  19. 1.6E: Rational Expressions (Exercises)
  20. 2: Equations and Inequalities
  21. 2.0: Prelude to Equations and Inequalities
  22. 2.1: The Rectangular Coordinate Systems and Graphs
  23. 2.1.0: The Rectangular Coordinate Systems and Graphs (Exercises)
  24. 2.2: Linear Equations in One Variable
  25. 2.2.0: Linear Equations in One Variable (Exercises)
  26. 2.3: Models and Applications
  27. 2.3.0: Models and Applications (Exercises)
  28. 2.4: Complex Numbers
  29. 2.4.0: Complex Numbers (Exercises)
  30. 2.5: Quadratic Equations
  31. 2.5.0: Quadratic Equations (Exercises)
  32. 2.6: Other Types of Equations
  33. 2.6.0: Other Types of Equations (Exercises)
  34. 2.7: Linear Inequalities and Absolute Value Inequalities
  35. 2.7.0: Linear Inequalities and Absolute Value Inequalities (Exercises)
  36. 3: Functions
  37. 3.0: Prelude to Functions
  38. 3.1: Functions and Function Notation
  39. 3.1E: Functions and Function Notation (Exercises)
  40. 3.2: Domain and Range
  41. 3.2E: Domain and Range (Exercises)
  42. 3.3: Rates of Change and Behavior of Graphs
  43. 3.3E: Rates of Change and Behavior of Graphs (Exercises)
  44. 3.4: Composition of Functions
  45. 3.4E: Composition of Functions (Exercises)
  46. 3.5: Transformation of Functions
  47. 3.5E: Transformation of Functions (Exercises)
  48. 3.6: Absolute Value Functions
  49. 3.6E: Absolute Value Functions (Exercises)
  50. 3.7: Inverse Functions
  51. 3.7E: Inverse Functions (Exercises)
  52. 4: Linear Functions
  53. 4.0: Introduction to Linear Functions
  54. 4.1: Linear Functions
  55. 4.1E: Linear Functions (Exercises)
  56. 4.2: Modeling with Linear Functions
  57. 4.2E: Modeling with Linear Functions (Exercises)
  58. 4.3: Fitting Linear Models to Data
  59. 4.3E: Fitting Linear Models to Data (Exercises)
  60. 5: Polynomial and Rational Functions
  61. 5.0: Prelude to Polynomial and Rational Functions
  62. 5.1: Quadratic Functions
  63. 5.1E: Quadratic Functions (Exercises)
  64. 5.2: Power Functions and Polynomial Functions
  65. 5.2E: Power Functions and Polynomial Functions (Exercises)
  66. 5.3: Graphs of Polynomial Functions
  67. 5.3E: Graphs of Polynomial Functions (Exercises)
  68. 5.4: Dividing Polynomials
  69. 5.4E: Dividing Polynomials (Exercises)
  70. 5.5: Zeros of Polynomial Functions
  71. 5.5E: Zeros of Polynomial Functions (Exercises)
  72. 5.6: Rational Functions
  73. 5.6E: Rational Functions (Exercises)
  74. 5.7: Inverses and Radical Functions
  75. 5.7E: Inverses and Radical Functions (Exercises)
  76. 5.8: Modeling Using Variation
  77. 5.8E: Modeling Using Variation (Exercises)
  78. 6: Exponential and Logarithmic Functions
  79. 6.0: Prelude to Exponential and Logarithmic Functions
  80. 6.1: Exponential Functions
  81. 6.1E: Exponential Functions (Exercises)
  82. 6.2: Graphs of Exponential Functions
  83. 6.2E: Graphs of Exponential Functions (Exercises)
  84. 6.3: Logarithmic Functions
  85. 6.3E: Logarithmic Functions (Exercises)
  86. 6.4: Graphs of Logarithmic Functions
  87. 6.4E: Graphs of Logarithmic Functions (Exercises)
  88. 6.5: Logarithmic Properties
  89. 6.5E: Logarithmic Properties (Exercises)
  90. 6.6: Exponential and Logarithmic Equations
  91. 6.6E: Exponential and Logarithmic Equations (Exercises)
  92. 6.7: Exponential and Logarithmic Models
  93. 6.7E: Exponential and Logarithmic Models (Exercises)
  94. 6.8: Fitting Exponential Models to Data
  95. 6.8E: Fitting Exponential Models to Data (Exercises)
  96. 7: The Unit Circle - Sine and Cosine Functions
  97. 7.0: Introduction to The Unit Circle- Sine and Cosine Functions
  98. 7.1: Angles
  99. 7.1E: Angles (Exercises)
  100. 7.2: Right Triangle Trigonometry
  101. 7.2E: Right Triangle Trigonometry (Exercises)
  102. 7.3: Unit Circle
  103. 7.3E: Unit Circle (Exercises)
  104. 7.4: The Other Trigonometric Functions
  105. 7.4E: The Other Trigonometric Functions (Exercises)
  106. 8: Periodic Functions
  107. 8.0: Introduction to Periodic Functions
  108. 8.1: Graphs of the Sine and Cosine Functions
  109. 8.1E: Graphs of the Sine and Cosine Functions (Exercises)
  110. 8.2: Graphs of the Other Trigonometric Functions
  111. 8.2E: Graphs of the Other Trigonometric Functions (Exercises)
  112. 8.3: Inverse Trigonometric Functions
  113. 8.3E: Inverse Trigonometric Functions (Exercises)
  114. 9: Trigonometric Identities and Equations
  115. 9.0: Prelude to Trigonometric Identities and Equations
  116. 9.1: Solving Trigonometric Equations with Identities
  117. 9.1E: Solving Trigonometric Equations with Identities (Exercises)
  118. 9.2: Sum and Difference Identities
  119. 9.2E: Sum and Difference Identities (Exercises)
  120. 9.3: Double-Angle, Half-Angle, and Reduction Formulas
  121. 9.3E: Double-Angle, Half-Angle, and Reduction Formulas (Exercises)
  122. 9.4: Sum-to-Product and Product-to-Sum Formulas
  123. 9.4E: Sum-to-Product and Product-to-Sum Formulas (Exercises)
  124. 9.5: Solving Trigonometric Equations
  125. 9.5E: Solving Trigonometric Equations (Exercises)
  126. 10: Further Applications of Trigonometry
  127. 10.0: Prelude to Further Applications of Trigonometry
  128. 10.1: Non-right Triangles - Law of Sines
  129. 10.1E: Non-right Triangles - Law of Sines (Exercises)
  130. 10.2: Non-right Triangles - Law of Cosines
  131. 10.2E: Non-right Triangles - Law of Cosines (Exercises)
  132. 10.3: Polar Coordinates
  133. 10.3E: Polar Coordinates (Exercises)
  134. 10.4: Polar Coordinates - Graphs
  135. 10.4E: Polar Coordinates - Graphs (Exercises)
  136. 10.5: Polar Form of Complex Numbers
  137. 10.5E: Polar Form of Complex Numbers (Exercises)
  138. 10.6: Parametric Equations
  139. 10.6E: Parametric Equations (Exercises)
  140. 10.7: Parametric Equations- Graphs
  141. 10.7E: Parametric Equations- Graphs (Exercises)
  142. 10.8: Vectors
  143. 10.8E: Vectors (Exercises)
  144. 11: Systems of Equations and Inequalities
  145. 11.0: Prelude to Systems of Equations and Inequalities
  146. 11.1: Systems of Linear Equations - Two Variables
  147. 11.1E: Systems of Linear Equations - Two Variables (Exercises)
  148. 11.2: Systems of Linear Equations with Three Variables
  149. 11.2E: Systems of Linear Equations with Three Variables (Exercises)
  150. 11.3: Systems of Nonlinear Equations and Inequalities - Two Variables
  151. 11.3E: Systems of Nonlinear Equations and Inequalities - Two Variables (Exercises)
  152. 11.4: Partial Fractions
  153. 11.4E: Partial Fractions (Exercises)
  154. 11.5: Matrices and Matrix Operations
  155. 11.5E: Matrices and Matrix Operations (Exercises)
  156. 11.6: Solving Systems with Gaussian Elimination
  157. 11.6E: Solving Systems with Gaussian Elimination (Exercises)
  158. 11.7: Solving Systems with Inverses
  159. 11.7E: Solving Systems with Inverses (Exercises)
  160. 11.8: Solving Systems with Cramer's Rule
  161. 11.8E: Solving Systems with Cramer's Rule (Exercises)
  162. 12: Analytic Geometry
  163. 12.0: Prelude to Analytic Geometry
  164. 12.1: The Ellipse
  165. 12.1E: The Ellipse (Exercises)
  166. 12.2: The Hyperbola
  167. 12.2E: The Hyperbola (Exercises)
  168. 12.3: The Parabola
  169. 12.3E: The Parabola (Exercises)
  170. 12.4: Rotation of Axes
  171. 12.4E: Rotation of Axes (Exercises)
  172. 12.5: Conic Sections in Polar Coordinates
  173. 12.5E: Conic Sections in Polar Coordinates (Exercises)
  174. 13: Sequences, Probability, and Counting Theory
  175. 13.0: Prelude to Sequences, Probability and Counting Theory
  176. 13.1: Sequences and Their Notations
  177. 13.1E: Sequences and Their Notations (Exercises)
  178. 13.2: Arithmetic Sequences
  179. 13.2E: Arithmetic Sequences (Exercises)
  180. 13.3: Geometric Sequences
  181. 13.3E: Geometric Sequences (Exercises)
  182. 13.4: Series and Their Notations
  183. 13.4E: Series and Their Notations (Exercises)
  184. 13.5: Counting Principles
  185. 13.5E: Counting Principles (Exercises)
  186. 13.6: Binomial Theorem
  187. 13.6E: Binomial Theorem (Exercises)
  188. 13.7: Probability
  189. 13.7E: Probability (Exercises)
  190. Back Matter
  191. Index
  192. Glossary
  193. Glossary
  194. Detailed Licensing