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    <option value="index.html">Introduction </option>
    <option value="who.html">Who should take this course? </option>
    <option value="apps.html">Applications of trigonometry </option>
    <option value="what.html">What is trigonometry? </option>
    <option value="geometry.html">Background on geometry </option>
    <option value="angle.html">Angle measurement </option>
    <option value="chords.html">Chords </option>
    <option value="sines.html">Sines </option>
    <option value="cosines.html">Cosines </option>
    <option value="tangents.html">Tangents and slope </option>
    <option value="right.html">The trigonometry of right triangles </option>
    <option value="functions.html">Trigonometric functions </option>
    <option value="compute.html">Computing trigonometric functions </option>
    <option value="oblique.html">The trigonometry of oblique triangles </option>
    <option value="laws.html">The laws of sines and cosines </option>
    <option value="area.html">Area of a triangle </option>
    <option value="ptolemy.html">Ptolemy's sum and difference formulas </option>
    <option value="formulas.html">Summary of trigonometric formulas </option>
    <option value="identities.html">Summary of trigonometric identities </option>
    <option value="last.html">The End </option>
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Text Content

DAVE’S SHORT TRIG COURSE







Table of Contents
 1.  Who should take this course?
     * Trigonometry for you
     * Your background
     * How to learn trigonometry
     
     

 2.  Applications of trigonometry
     * Astronomy and geography
     * Engineering and physics
     * Mathematics and its applications
     
     

 3.  What is trigonometry?
     * Trigonometry as computational geometry
     * Angle measurement and tables
     
     

 4.  Background on geometry
     * The Pythagorean theorem
     * An explanation of the Pythagorean theorem
     * Similar triangles
     
     

 5.  Angle measurement
     * The concept of angle
     * Radians and arc length
     * Exercises, hints, and answers
     * About digits of accuracy
     
     

 6.  Chords
     * What is a chord?
     * Trigonometry began with chords
     
     

 7.  Sines
     * The relation between sines and chords
     * The word “sine”
     * Sines and right triangles
     * The standard notation for a right triangle
     * Exercises, hints, and answers
     
     

 8.  Cosines
     * Definition of cosine
     * Right triangles and cosines
     * The Pythagorean identity for sines and cosines
     * Sines and cosines for special common angles
     * Exercises, hints, and answers
     
     

 9.  Tangents and slope
     * The definition of the tangent
     * Tangent in terms of sine and cosine
     * Tangents and right triangles
     * Slopes of lines
     * Angles of elevation and depression
     * Common angles again
     * Exercises, hints, and answers
     
     

 10. The trigonometry of right triangles
     * Solving right triangles
     * Inverse trig functions: arcsine, arccosine, and arctangent
     * The other three trigonometric functions: cotangent, secant, and cosecant
     * Exercises, hints, and answers
     * Pythagorean triples
     
     

 11. The trigonometric functions and their inverses
     * Arbitrary angles and the unit circle
     * Sines and cosines of arbitrary angles
     * Properties of sines and cosines that follow from the definition
     * Graphs of sine and cosine functions
     * Graphs of tangent and cotangent functions
     * Graphs of secant and cosecant functions
     
     

 12. Computing trigonometric functions
     * Before computers: tables
     * After computers: power series
     
     

 13. The trigonometry of oblique triangles
     * Solving oblique triangles
     * The law of cosines
     * The law of sines
     * Exercises, hints, and answers
     
     

 14. Demonstrations of the laws of sines and cosines
     * For the law of sines
     * For the law of cosines
     
     

 15. Area of a triangle
     * Area in terms of two sides and the included angle
     
     

 16. Ptolemy’s sum and difference formulas
     * Ptolemy’s theorem
     * The sum formula for sines
     * The other sum and difference formulas
     
     

 17. Summary of trigonometric formulas
     * Formulas for arcs and sectors of circles
     * Formulas for right triangles
     * Formulas for oblique triangles
     * Formulas for areas of triangles
     
     

 18. Summary of trigonometric identities
     * More important identities
     * Less important identities
     * Truly obscure identities



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Select topicIntroduction Who should take this course? Applications of
trigonometry What is trigonometry? Background on geometry Angle measurement
Chords Sines Cosines Tangents and slope The trigonometry of right triangles
Trigonometric functions Computing trigonometric functions The trigonometry of
oblique triangles The laws of sines and cosines Area of a triangle Ptolemy's sum
and difference formulas Summary of trigonometric formulas Summary of
trigonometric identities The End

Dave’s Short Trig Course is located
at http://www.clarku.edu/~djoyce/trig©1996, 1997, 2002, 2013
David E. Joyce

Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610