# Honors Trigonometry

Prerequisites: Qualifying math score and successful completion of Algebra II or equivalent

Course Format: Individually Paced

Course Length: Typically 3 months

Recommended School Credit: One academic year

Course Code: TRI

## Course Description

Description

CTY Online Programs's 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.

## 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
• Composite Functions
• Rational Functions
• Graphing Rational Functions
• Function Inverses
• Finding Function Inverses

### The Trigonometric Functions

• 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

### 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