Trigonometry
**Available with Ultimate Membership Only**
Length: 63 Lessons
Includes: Worksheets with Assignments
Age/Grade: High School
View a Sample of Trigonometry
Print a Certificate of Completion
How to Use This Course
This in-depth trigonometry course provides more than sixty lessons that include ample illustrations, multiple assignments, and step-by-step solutions as well as gradable tests. Answer keys are included, and Mrs. Candler is available to answer questions by email (see contact information on page 3 of the course download).
Course Introduction
This semester-long course is a thorough trigonometry course that can be done in several ways. Students who are pursuing a math-intensive degree may wish to take this class in the eighteen weeks as it is laid out and follow it with another semester-long math class, such as Introduction to Statistics. Students who are pursuing a less math-intensive field may want to spread this course out over more than eighteen weeks, as it is a meaty course with ample practice problems and assignments.
Course Outline
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
This is a one-semester high school trigonometry course worth one-half credit in math upon successful completion of all assignments.
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