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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. This course does not have any synchronous class meetings, but students may schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. 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.

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Materials Needed

Graphing calculator recommended, such as:

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

List of Topics


  • Radian and Degree Measure
  • Trigonometric Functions: The Unit Circle
  • Right Triangle Trigonometry
  • Trigonometric Functions of Any Angle
  • Graphs of Sine and Cosine Functions
  • Graph of Other Trigonometric Functions
  • Inverse Trigonometric Functions
  • Applications and Models

Analytic Trigonometry

  • Using Fundamental Identities
  • Verifying Trigonometric Identities
  • Solving Trigonometry Equations
  • Sum and Difference Formulas
  • Multiple-Angle and Product-to-Sum Formulas
  • Additional Topics in Trigonometry
  • Law of Sines
  • Law of Cosines
  • Vectors in the Plane
  • Vectors and Dot Products

Complex Numbers

  • Complex Numbers
  • Complex Solutions to Equations
  • The Complex Plane
  • Trigonometric Form of a Complex Number
  • DeMoivre's Theorem

Exponential and Logarithmic Functions

  • Exponential Functions and Their Graphs
  • Logarithmic Functions and Their Graphs
  • Properties of Logarithms
  • Exponential and Logarithmic Equations
  • Exponential and Logarithmic Models

Topics in Analytic Geometry

  • Lines
  • Introduction to Conics: Parabolas
  • Ellipses
  • Hyperbolas
  • Rotation of Conics
  • Parametric Equations
  • Polar Coordinates
  • Graphs of Polar Equations
  • Polar Equations of Conics

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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 which can be used for instructor-student communication if the student has any questions about the course or curriculum. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students will need a computer with the Zoom desktop client installed to watch any 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.

Electronic Texbook (eBook) and WebAssign Online Homework System: This course requires the use of WebAssign for online homework and access to the electronic textbook. Visit the WebAssign website for system requirements.