Dave's Short Trig Course


Table of Contents
  1. Who should take this course?
  2. Trigonometry for you
  3. Your background
  4. How to learn trigonometry
  5. Applications of trigonometry
  6. Astronomy and geography
  7. Engineering and physics
  8. Mathematics and its applications
  9. What is trigonometry?
  10. Trigonometry as computational geometry
  11. Angle measurement and tables
  12. Background on geometry
  13. The Pythagorean theorem
  14. An explanation of the Pythagorean theorem
  15. Similar triangles
  16. Angle measurement
  17. The concept of angle
  18. Radians and arc length
  19. Exercises, hints, and answers
  20. About digits of accuracy
  21. Chords
  22. What is a chord?
  23. Trigonometry began with chords
  24. Sines
  25. The relation between sines and chords
  26. The word "sine"
  27. Sines and right triangles
  28. The standard notation for a right triangle
  29. Exercises, hints, and answers
  30. Cosines
  31. Definition of cosine
  32. Right triangles and cosines
  33. The Pythagorean identity for sines and cosines
  34. Sines and cosines for special common angles
  35. Exercises, hints, and answers
  36. Tangents and slope
  37. The definition of the tangent
  38. Tangent in terms of sine and cosine
  39. Tangents and right triangles
  40. Slopes of lines
  41. Angles of elevation and depression
  42. Common angles again
  43. Exercises, hints, and answers
  44. The trigonometry of right triangles
  45. Solving right triangles
  46. Inverse trig functions: arcsine, arccosine, and arctangent
  47. The other three trigonometric functions: cotangent, secant, and cosecant
  48. Exercises, hints, and answers
  49. Pythagorean triples
  50. The trigonometric functions and their inverses
  51. Arbitrary angles and the unit circle
  52. Sines and cosines of arbitrary angles
  53. Properties of sines and cosines that follow from the definition
  54. Graphs of sine and cosine functions
  55. Graphs of tangent and cotangent functions
  56. Graphs of secant and cosecant functions
  57. Computing trigonometric functions
  58. Before computers: tables
  59. After computers: power series
  60. The trigonometry of oblique triangles
  61. Solving oblique triangles
  62. The law of cosines
  63. The law of sines
  64. Exercises, hints, and answers
  65. Demonstrations of the laws of sines and cosines
  66. For the law of sines
  67. For the law of cosines
  68. Area of a triangle
  69. Area in terms of two sides and the included angle
  70. Summary of trigonometric identities
  71. More important identities
  72. Less important identities
  73. Truly obscure identities
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Special symbols used here. Some old web browsers do not display mathematical symbols. The following table shows the mathematical symbols used here. If there are any entries in the first column that appear blank or appear as question marks, then your web browser will not display those symbols, and you will need to use a different web browser to see all the symbols.

Symbol / Description / Example
– / minus sign / x–y
± / plus or minus sign / x±y
° / degree sign / 45°
√ / square root sign / √2
3√ / cube root sign / 3√5
≠ / not equal to / x≠y
≤ / less than or equal to / x≤y
≥ / greater than or equal to / x≥y

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Started July, 1996. Copyright © 1996, 1997, 2002.

David E. Joyce
Department of Mathematics and Computer Science
Clark University Worcester, MA 01610

Dave's Short Trig Course is located at