Lesson 1: Trigonometric Ratios of Any Angle

• Review of key definitions and explanations

  • Standard position

  • Initial arm

  • Terminal arm

• Trigonometric ratios on Cartesian Plane

  • Trigonometric ratios in each quadrant

  • The CAST rule

• Signs of trigonometric ratios on the Cartesian Plane

• Special triangles

  • Exact values

• Special triangles and quadrant relationship

• Solving for exact values of trigonometric ratios

  • Steps to finding exact values of trigonometric ratios

Lesson 2: Graphing Trigonometric Functions

• Primary Sine function

• Explanation of key components:

  • Domain, range, period, minimum, maximum, x- & y- intercepts

• Primary Cosine function

• Explanation of key components:

  • Domain, range, period, minimum, maximum, x- & y- intercepts

• Period of Sine & Cosine functions

  • Definition of period

  • Explanation of horizontal compression / stretch

  • Explanation of negative “k”

• Solutions to examples explained

Lesson 3: Amplitude of Sine and Cosine Functions

• Defining amplitude

• Amplitude formula

• Amplitude symbol

• Vertical compression / stretch, and reflection

• Graphing of functions explained

• Calculating maximum & minimum, domain & range, y-intercept

• Graphing combination of “k” factor and amplitude functions

• Vertical translation of/sine & Cosine functions

• Horizontal translation of/sine & Cosine functions

• Calculating components for both functions

• Combining transformations

  • General equations for Sine and Cosine explained

• 5 Steps to graph combined transformation functions

• Example of graphing a combined transformation function

• Given the equation of a function, how to find the characteristics

Lesson 4: Reciprocal Trigonometric Functions

• Recall Primary trigonometric ratios

• Reciprocal trigonometric ratios explained

• Summary of angles of Special Triangles

• CAST rule for reciprocal trigonometric functions

• Examples of solving for exact values

• Solving more difficult reciprocal trigonometric ratios

• Trigonometric Identities

  • Defining an identity

• Common trigonometric identities:

  • Pythagorean identity

  • Quotient identity

  • Reciprocal identities

• Proving Trigonometric Identities:

  • Main goal

  • 3 steps to use

• Solutions for examples proving trigonometric identities

Here are a few sample questions for you to practice. The answers are given at the end.