Math 373: Trigonometry for Calculus

by Roy Simpson

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This course provides a rigorous treatment of trigonometry and its applications, focusing on preparing students for the calculus sequence for STEM majors. Topics include right triangle trigonometry, unit circle trigonometry, graphs of trigonometric functions, proofs of trigonometric identities, solving trigonometric equations, applications of trigonometric functions (laws of sines and cosines), inverse trigonometric functions, the polar coordinate system, and an introduction to vectors.

Description from LibreTexts.

Publisher
Cosumnes River College
Subjects
Mathematics
Licence
CC BY-SA, 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. Foreword to the Instructor
  6. Licensing
  7. Templates
  8. Licensing
  9. 1: Triangles and Circles
  10. 1.1: Angles and Basic Geometry
  11. 1.1.1: Resources and Key Concepts
  12. 1.1.2: Homework
  13. 1.2: Triangles
  14. 1.2.1: Resources and Key Concepts
  15. 1.2.2: Homework
  16. 1.3: Similar Triangles
  17. 1.3.1: Resources and Key Concepts
  18. 1.3.2: Homework
  19. 1.4: Circles and Angles in the Rectangular Coordinate System
  20. 1.4.1: Resources and Key Concepts
  21. 1.4.2: Homework
  22. 2: Coordinate Trigonometry
  23. 2.1: The Trigonometric Functions - Coordinate Definition
  24. 2.1.1: Resources and Key Concepts
  25. 2.1.2: Homework
  26. 2.2: Algebra with Trigonometric Functions
  27. 2.2.1: Resources and Key Concepts
  28. 2.2.2: Homework
  29. 2.3: Introduction to Trigonometric Identities
  30. 2.3.1: Resources and Key Concepts
  31. 2.3.2: Homework
  32. 2.4: Introduction to Proofs in Trigonometry
  33. 2.4.1: Resources and Key Concepts
  34. 2.4.2: Homework
  35. 3: Right Triangle Trigonometry
  36. 3.1: The Trigonometric Functions - Right Triangle Definition
  37. 3.1.1: Resources and Key Concepts
  38. 3.1.2: Homework
  39. 3.2: Technology and Right Triangle Trigonometry
  40. 3.2.1: Resources and Key Concepts
  41. 3.2.2: Homework
  42. 3.3: Solving Right Triangles
  43. 3.3.1: Resources and Key Concepts
  44. 3.3.2: Homework
  45. 3.4: Applications Involving Right Triangles
  46. 3.4.1: Resources and Key Concepts
  47. 3.4.2: Homework
  48. 4: Radian Measure and the Circular Functions
  49. 4.1: Reference Angles
  50. 4.1.1: Resources and Key Concepts
  51. 4.1.2: Homework
  52. 4.2: Radian Measure and Arc Length
  53. 4.2.1: Resources and Key Concepts
  54. 4.2.2: Homework
  55. 4.3: The Trigonometric Functions - Unit Circle Definition
  56. 4.3.1: Resources and Key Concepts
  57. 4.3.2: Homework
  58. 4.4: Velocities and Areas of Sectors
  59. 4.4.1: Resources and Key Concepts
  60. 4.4.2: Homework
  61. 5: Graphs of the Trigonometric Functions
  62. 5.1: Base Graphs of the Fundamental Trigonometric Functions
  63. 5.1.1: Resources and Key Concepts
  64. 5.1.2: Homework
  65. 5.2: Non-Rigid Transformations
  66. 5.2.1: Resources and Key Concepts
  67. 5.2.2: Homework
  68. 5.3: Rigid Transformations
  69. 5.3.1: Resources and Key Concepts
  70. 5.3.2: Homework
  71. 5.4: Sinusoidal Models
  72. 5.4.1: Resources and Key Concepts
  73. 5.4.2: Homework
  74. 5.5: Harmonic Motion
  75. 5.5.1: Resources and Key Concepts
  76. 5.5.2: Homework
  77. 5.6: Graphs of the Remaining Trigonometric Functions
  78. 5.6.1: Resources and Key Concepts
  79. 5.6.2: Homework
  80. 6: Analytic Trigonometry
  81. 6.1: Basic Trigonometric Identities and Proof Techniques
  82. 6.1.1: Resources and Key Concepts
  83. 6.1.2: Homework
  84. 6.2: Sum and Difference Identities
  85. 6.2.1: Resources and Key Concepts
  86. 6.2.2: Homework
  87. 6.3: Double-Angle Identities
  88. 6.3.1: Resources and Key Concepts
  89. 6.3.2: Homework
  90. 6.4: Half-Angle and Power Reduction Identities
  91. 6.4.1: Resources and Key Concepts
  92. 6.4.2: Homework
  93. 6.5: Sum-to-Product and Product-to-Sum Identities
  94. 6.5.1: Resources and Key Concepts
  95. 6.5.2: Homework
  96. 7: Trigonometric Equations
  97. 7.1: The Fundamental Inverse Trigonometric Functions
  98. 7.1.1: Resources and Key Concepts
  99. 7.1.2: Homework
  100. 7.2: The Remaining Inverse Trigonometric Functions
  101. 7.2.1: Resources and Key Concepts
  102. 7.2.2: Homework
  103. 7.3: Solving Trigonometric Equations - Algebraic Techniques
  104. 7.3.1: Resources and Key Concepts
  105. 7.3.2: Homework
  106. 7.4: Solving Trigonometric Equations Using Identities
  107. 7.4.1: Resources and Key Concepts
  108. 7.4.2: Homework
  109. 8: Non-Right Triangle Trigonometry
  110. 8.1: The Law of Sines
  111. 8.1.1: Resources and Key Concepts
  112. 8.1.2: Homework
  113. 8.2: The Law of Cosines
  114. 8.2.1: Resources and Key Concepts
  115. 8.2.2: Homework
  116. 8.3: Areas
  117. 8.3.1: Resources and Key Concepts
  118. 8.3.2: Homework
  119. 8.4: Vectors - A Geometric Approach
  120. 8.4.1: Resources and Key Concepts
  121. 8.4.2: Homework
  122. 8.5: Vectors - An Algebraic Approach
  123. 8.5.1: Resources and Key Concepts
  124. 8.5.2: Homework
  125. 9: Polar Coordinates and Complex Numbers
  126. 9.1: Polar Coordinates
  127. 9.1.1: Resources and Key Concepts
  128. 9.1.2: Homework
  129. 9.2: Polar Graphs
  130. 9.2.1: Resources and Key Concepts
  131. 9.2.2: Homework
  132. 9.3: Complex Numbers
  133. 9.3.1: Resources and Key Concepts
  134. 9.3.2: Homework
  135. 9.4: Polar Form of Complex Numbers
  136. 9.4.1: Resources and Key Concepts
  137. 9.4.2: Homework
  138. 10: The Language of Mathematics
  139. 10.1: Definitions
  140. 10.2: Axioms, Theorems, and Proofs
  141. 10.3: Operations
  142. 10.4: Simplifying
  143. 10.5: Theory versus Application
  144. 10.6: The Mathematical Mantra
  145. Back Matter
  146. Index
  147. Glossary
  148. Detailed Licensing
  149. Detailed Licensing