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Math 373: Trigonometry for Calculus

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Math 373: Trigonometry for Calculus

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.

Mathematics
Author
Roy Simpson
Publisher
Cosumnes River College
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 136 sections
  1. 01: Triangles and Circles
  2. 1.01: Angles and Basic Geometry
  3. 1.1.01: Resources and Key Concepts
  4. 1.1.02: Homework
  5. 1.02: Triangles
  6. 1.2.01: Resources and Key Concepts
  7. 1.2.02: Homework
  8. 1.03: Similar Triangles
  9. 1.3.01: Resources and Key Concepts
  10. 1.3.02: Homework
  11. 1.04: Circles and Angles in the Rectangular Coordinate System
  12. 1.4.01: Resources and Key Concepts
  13. 1.4.02: Homework
  14. 02: Coordinate Trigonometry
  15. 2.01: The Trigonometric Functions - Coordinate Definition
  16. 2.1.01: Resources and Key Concepts
  17. 2.1.02: Homework
  18. 2.02: Algebra with Trigonometric Functions
  19. 2.2.01: Resources and Key Concepts
  20. 2.2.02: Homework
  21. 2.03: Introduction to Trigonometric Identities
  22. 2.3.01: Resources and Key Concepts
  23. 2.3.02: Homework
  24. 2.04: Introduction to Proofs in Trigonometry
  25. 2.4.01: Resources and Key Concepts
  26. 2.4.02: Homework
  27. 03: Right Triangle Trigonometry
  28. 3.01: The Trigonometric Functions - Right Triangle Definition
  29. 3.1.01: Resources and Key Concepts
  30. 3.1.02: Homework
  31. 3.02: Technology and Right Triangle Trigonometry
  32. 3.2.01: Resources and Key Concepts
  33. 3.2.02: Homework
  34. 3.03: Solving Right Triangles
  35. 3.3.01: Resources and Key Concepts
  36. 3.3.02: Homework
  37. 3.04: Applications Involving Right Triangles
  38. 3.4.01: Resources and Key Concepts
  39. 3.4.02: Homework
  40. 04: Radian Measure and the Circular Functions
  41. 4.01: Reference Angles
  42. 4.1.01: Resources and Key Concepts
  43. 4.1.02: Homework
  44. 4.02: Radian Measure and Arc Length
  45. 4.2.01: Resources and Key Concepts
  46. 4.2.02: Homework
  47. 4.03: The Trigonometric Functions - Unit Circle Definition
  48. 4.3.01: Resources and Key Concepts
  49. 4.3.02: Homework
  50. 4.04: Velocities and Areas of Sectors
  51. 4.4.01: Resources and Key Concepts
  52. 4.4.02: Homework
  53. 05: Graphs of the Trigonometric Functions
  54. 5.01: Base Graphs of the Fundamental Trigonometric Functions
  55. 5.1.01: Resources and Key Concepts
  56. 5.1.02: Homework
  57. 5.02: Non-Rigid Transformations
  58. 5.2.01: Resources and Key Concepts
  59. 5.2.02: Homework
  60. 5.03: Rigid Transformations
  61. 5.3.01: Resources and Key Concepts
  62. 5.3.02: Homework
  63. 5.04: Sinusoidal Models
  64. 5.4.01: Resources and Key Concepts
  65. 5.4.02: Homework
  66. 5.05: Harmonic Motion
  67. 5.5.01: Resources and Key Concepts
  68. 5.5.02: Homework
  69. 5.06: Graphs of the Remaining Trigonometric Functions
  70. 5.6.01: Resources and Key Concepts
  71. 5.6.02: Homework
  72. 06: Analytic Trigonometry
  73. 6.01: Basic Trigonometric Identities and Proof Techniques
  74. 6.1.01: Resources and Key Concepts
  75. 6.1.02: Homework
  76. 6.02: Sum and Difference Identities
  77. 6.2.01: Resources and Key Concepts
  78. 6.2.02: Homework
  79. 6.03: Double-Angle Identities
  80. 6.3.01: Resources and Key Concepts
  81. 6.3.02: Homework
  82. 6.04: Half-Angle and Power Reduction Identities
  83. 6.4.01: Resources and Key Concepts
  84. 6.4.02: Homework
  85. 6.05: Sum-to-Product and Product-to-Sum Identities
  86. 6.5.01: Resources and Key Concepts
  87. 6.5.02: Homework
  88. 07: Trigonometric Equations
  89. 7.01: The Fundamental Inverse Trigonometric Functions
  90. 7.1.01: Resources and Key Concepts
  91. 7.1.02: Homework
  92. 7.02: The Remaining Inverse Trigonometric Functions
  93. 7.2.01: Resources and Key Concepts
  94. 7.2.02: Homework
  95. 7.03: Solving Trigonometric Equations - Algebraic Techniques
  96. 7.3.01: Resources and Key Concepts
  97. 7.3.02: Homework
  98. 7.04: Solving Trigonometric Equations Using Identities
  99. 7.4.01: Resources and Key Concepts
  100. 7.4.02: Homework
  101. 08: Non-Right Triangle Trigonometry
  102. 8.01: The Law of Sines
  103. 8.1.01: Resources and Key Concepts
  104. 8.1.02: Homework
  105. 8.02: The Law of Cosines
  106. 8.2.01: Resources and Key Concepts
  107. 8.2.02: Homework
  108. 8.03: Areas
  109. 8.3.01: Resources and Key Concepts
  110. 8.3.02: Homework
  111. 8.04: Vectors - A Geometric Approach
  112. 8.4.01: Resources and Key Concepts
  113. 8.4.02: Homework
  114. 8.05: Vectors - An Algebraic Approach
  115. 8.5.01: Resources and Key Concepts
  116. 8.5.02: Homework
  117. 09: Polar Coordinates and Complex Numbers
  118. 9.01: Polar Coordinates
  119. 9.1.01: Resources and Key Concepts
  120. 9.1.02: Homework
  121. 9.02: Polar Graphs
  122. 9.2.01: Resources and Key Concepts
  123. 9.2.02: Homework
  124. 9.03: Complex Numbers
  125. 9.3.01: Resources and Key Concepts
  126. 9.3.02: Homework
  127. 9.04: Polar Form of Complex Numbers
  128. 9.4.01: Resources and Key Concepts
  129. 9.4.02: Homework
  130. 10: The Language of Mathematics
  131. 10.01: Definitions
  132. 10.02: Axioms Theorems and Proofs
  133. 10.03: Operations
  134. 10.04: Simplifying
  135. 10.05: Theory versus Application
  136. 10.06: The Mathematical Mantra