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Honors Trigonometry

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Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Algebra II or equivalent

Course Format: Individually Paced

Course Length: Typically 3 months

Recommended School Credit: One full year of high school credit

Course Code: TRI

Course Description


CTY Online Programs Honors Trigonometry is designed to be taken after the completion of Algebra II and is designed for students who are looking to better understand trigonometric functions in preparation for their studies of Calculus or Statistics. This comprehensive course reviews topics in Algebra II, and covers advanced topics in Trigonometry not often seen before Precalculus.

Students will learn trigonometry by actively engaging with the lectures, notes, project, and resources within the course website. As with every CTY Online Programs course, each student is assigned an instructor to help them throughout their enrollment. The instructor will provide individualized feedback, meet online one-on-one in a virtual classroom as needed, and provide motivation and support at all points in the course.

Students can progress at their own rate through this individually paced course. Student knowledge will be assessed by the completion of homework, exams and a project.   Graphing calculators are used throughout the course.

Honors Trigonometry Course Objectives:

  • The student will analyze, apply, and illustrate the properties of the unit circle.
  • The student will determine trigonometric values, calculate the transformations of trigonometric functions and graph trigonometric functions on the coordinate plane.
  • The student will utilize and apply trigonometric identities.
  • The student will use trigonometry to operate on complex numbers.
  • The student will study advanced topics in analytic geometry through trigonometric techniques.

For a detailed list of topics, click the List of Topics tab.

Honors Trigonometry Banner

Materials Needed

Graphing calculator recommended, such as:

  • TI-83 PLUS
  • TI-84 PLUS
  • TI-85
  • TI-86

List of Topics

Algebraic Prerequisites

  • Graphing Basics
  • Relationships between Two Points
  • Relationships among Three Points
  • Graphing Equations
  • Function Basics
  • Working with Functions
  • Function Domain and Range
  • Linear Functions: Slope
  • Equations of a Line
  • Graphing Functions
  • Manipulating Graphs: Shifts and Stretches
  • Manipulating Graphs: Symmetry and Reflections
  • Quadratic Functions: Basics
  • Quadratic Functions
  • Composite Functions
  • Rational Functions
  • Graphing Rational Functions
  • Function Inverses
  • Finding Function Inverses

The Trigonometric Functions

  • Angles and Radian Measure
  • Right Angle Trigonometry
  • Applications of Right Triangle Trigonometry
  • The Trigonometric Functions
  • Graphing Sine and Cosine Functions
  • Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts
  • Graphing Other Trigonometric Functions
  • Inverse Trigonometric Functions

Trigonometric Identities

  • Basic Trigonometric Identities
  • Simplifying Trigonometric Expressions
  • Proving Trigonometric Identities
  • Solving Trigonometric Equations
  • The Sum and Difference Identities
  • Double-Angle Identities
  • Other Advanced Identities

Applications of Trigonometry

  • The Law of Sines
  • The Law of Cosines
  • Heron's Formula
  • Vector Basics
  • Components of Vectors and Unit Vectors

Complex Numbers and Polar Coordinates

  • Complex Numbers
  • Operations on Complex Numbers
  • Complex Numbers in Trigonometric Form
  • Powers and Roots of Complex Numbers
  • Polar Coordinates

Topics in Analytic Geometry

  • Parabolas
  • Ellipses
  • Hyperbolas
  • Identifying Conic Sections
  • Rotation of Conics
  • Parametric Equations
  • Graphs of Polar Equations
  • Polar Equations of Conics

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Sample Video

Precalculus with Professor Edward Burger - Using Trig to solve a world problem

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

Zoom online virtual classroom
This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.