Right Triangle Trigonometry

• Trigonometric Functions Defined in a Right Triangle
• Special Right Triangles
• The Beginning of Trigonometric Identities
• Applications Involving Right Triangles

From Acute Angles to Any Angle

• Degree Measure
• Radian Measure
• Trigonometric Functions of Any Angle (Circular Functions)
• Reference Angles
• Making Connections with Special Angles

From Any Angle to All Real Numbers

• Using the Unit Circle
• The Trigonometric Functions of Real Numbers
• Putting It All Together

Graphing the Sine and Cosine Functions

• The Basic Sine and Cosine Functions
• Graphing the Sine Function in the Form y=a sin bx
• Graphing the Sine Function in the Form y=a sin(bx+c)+d
• Graphing the Cosine Function in the Form y=a cos (bx+c)+d
• Working Through an Application of Sine or Cosine
• Applications with Graph Variations

Graphing the Other Trigonometric Functions

• The Basic Tangent Function
• Graphing the Tangent Function in the Form y=a tan (bx+c)+d
• Graphing the Reciprocal Functions
• The Inverse Sine Function
• The Inverse Cosine and Inverse Tangent Functions
• Composition of Inverse Functions

Working with Identities

• Fundamental Identities
• Simplifying Expressions by Basic Substitution
• Simplifying by Factoring
• Simplifying by Combining Fractions
• Verifying Identities by Basic Substitution
• Verifying Identities by Factoring
• Verifying Identities by Converting to Sines and Cosines
• Verifying Identities by Combining Fractions

Solving Trigonometric Equations

• Solving Basic Trigonometric Equations
• Solving by Square Roots or Squaring
• Solving by Common Factors or Difference of Two Squares
• Solving by Trinomial Factoring
• Solving Equations with Multiple Angles

More Trigonometric Equations and New Identities

• Finding Approximate Solutions to Equations
• Mixing up the Equations
• The Sum and Difference Formulas
• Using the Sum/Difference Formulas with Past Concepts
• Verifying Identities Using Sum/Difference Formulas
• The Double Angle Formulas
• The Half-Angle Formulas
• Solving Equations with Multiple Angles
• The Remaining Identities

Oblique Triangle Applications

• The Law of Sines
• Law of Sines Applications
• Applications with Bearings
• The Area of an Oblique Triangle
• The Law of Cosines
• Applications for the Law of Cosines
• Heron’s Formula for the Area of a Triangle

Other Trigonometry Applications

• Basic Properties of Vectors
• More About Vectors
• Vector Applications
• Trigonometric Form of a Complex Number
• Multiplication, Division, and Powers of a Complex Number
• Roots of a Complex Number
• The Polar Coordinate System (Plotting Points)
• Graphing Polar Equations
• From Polar to Rectangular and Vice Versa
• Final Lesson

Download the Trigonometry syllabus here.

This is a one-semester high school trigonometry course worth one-half credit in math upon successful completion of all assignments. You may wish to have your student also do our one-semester high school statistics course that is also worth one-half credit to complete the year of high school math.