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I. What is Trigonometry?

  1. Angular Nomiclature
  2. Circular Nomiclature
  3. Basic Trigonometric Functions

II. Cartesian Frames of Reference

  1. Pythagorean’s Theorem
    1. The Distance Formula
  2. Midpoint of a Line Segment
  3. Centroid of a Triangle
  4. Circumscribing a Triangle
  5. Slope and Intercept
  6. Parallel and Perpendicular Lines

III. Measuring Angles

  1. Decimal Degrees
  2. Degrees, [arc] Seconds
  3. Radians
  4. Angles and Real-World Applications

IV. Right Triangle

  1. The 30°-60° – 90° triangle
  2. The Right Isosceles Triangle
  3. Trig Functions and the Right Triangle
    1. Sine
    2. Cosine
    3. Tangent
  4. Completing the Unknowns of a Triangle

V. Relating Triangles to Circular Functions

  1. The Unit Circle
  2. Cyclic Quadrilateral
  3. Unit Circle Coordinates & Trig Solutions
  4. Relationships Between the Functions
  5. The Versine

VI. Applications of Trigonometric Functions

  1. Heron’s Formula for the Area of a Triangle

VII. Trigonometric Identities

  1. Sum Angle Identities
  2. Differences of Angles identities
  3. Double Angle Identities
  4. Half-Angle Identities
  5. Proof of Identities
  6. Using Identities to Simplify Algebra

VIII Inverse Trigonometric Functions

  1. Domains and Ranges of Inverse Functions

IX. Solving for the Sides and Angles of a Triangle

  1. Law of sines
  2. Law of Cosines
  3. The inverse of the Dot Product
  4. Areas of Triangles

X. The Graphing of Trigonometric Functions

  1. Shifting and Displaying Cyclic Functions