 # Trigonometry

9-12

Course Outline

This course will focus on the study of angles; the trigonometry of angles and real numbers; the trigonometric functions and their inverses including their graphs; solutions of right and oblique triangles; verification of fundamental identities and analytic trigonometry; addition, subtraction and multiple angle formulas; the laws of sines and cosines; vectors and the dot and cross product; complex numbers, De Moivre’s Theorem and nth roots of complex numbers; polar coordinates and equations. The course will also include the study of functions including exponential and logarithmic functions.

TRIGONOMETRIC FUNCTIONS

• Extend the domain of trigonometric functions using the unit circle

• Model periodic phenomena with trigonometric functions

• Prove and apply trigonometric identities

THE COMPLEX NUMBER SYSTEM

• Perform arithmetic operations with complex numbers

• Represent complex numbers and their operations on the complex plane

• Use complex numbers in polynomial identies and equations

VECTOR & MATRIX QUANTITIES

• Represent and model with vector quantities

• Perform operations on vectors

SIMILARITY, RIGHT TRIANGLES TRIGONOMETRY

• Define trigonometric ratios and solve problems involving right triangles

• Apply trigonometry to general triangles

1. Angles & Triangles

Angles and Angle Measures:

• Handout: Angles & Angle Measures Worksheet

• Assignment: Angles & Angle Measures

• Worksheet: Converting Angle Measures

Triangle Review:

• Handout: Triangle Review Worksheet

• Assignment: Triangle Review

Pythagorean Theorem:

• Handout: Pythagorean Theorem Worksheet

• Assignment: Pythagorean Theorem

Special Right Triangles:

• Handout: Special Right Triangles Worksheet

• Assignment: Special Right Triangles

Basic Trigonometric Ratios:

• Handout: Basic Trigonometric Ratios Worksheet

• Assignment: Basic Trigonometric Ratios

Inverse Trigonometric Ratios:

• Worksheet: Inverse Trigonometric Ratios

Laws of Sine & Cosine:

• Handout: Law of Sines & Cosines Worksheet

• Assignment: Law of Sines & Cosines

The Unit Circle:

• Handout: Unit Circle

• Handout: Finding Trig Values

• Handout: Evaluating Trig Functions Worksheet

• Assignment: Evaluating Trig Functions

1. Graphs of Trigonometric Functions

Graphs of Sine & Cosine:

• Handout: Graphs of Sine & Cosine Worksheet

• Assignment: Graphs of Sine & Cosine

Linear & Angular Velocity:

• Handout: Linear & Angular Velocity Worksheet

• Assignment: Linear & Angular Velocity

Graphs of Other Trig Functions:

• Handout: Cotangent Graph Exploration

• Assignment: Cotangent Graph Exploration

Translations of Trig Functions:

• Handout: Translations of Trig Functions Worksheet

• Assignment: Translations of Trig Functions

Applications of Trig Functions:

• Handout: Sinusoidal Applications Worksheet

• Essay: Real-World Applications

• Assignment: Sinusoidal Applications

1. Trigonometric Identities

Fundamental Trigonometric Identities:

• Handout: Fundamental Trigonometric Identities Worksheet

• Assignment: Fundamental Trigonometric Identities

Proving Trigonometric Identities:

• Handout: Proving Trig Identities Worksheet

• Assignment: Proving Trig Identities

Sum & Difference Identities:

• Handout: Sum & Difference Identities Worksheet

• Assignment: Sum & Difference Identities

• Essay: Sum & Difference Identities Short Answer

Double-Angle & Half-Angle Identities:

• Handout: Double & Half-Angle Identities Worksheet

• Assignment: Double & Half-Angle Identities

• Essay: Double & Half-Angle Identities Short Answer

Solving Trigonometric Equations:

• Handout: Solving Trig Equations Worksheet

• Assignment: Solving Trig Equations

1. Mid-Term Exam

• Assignment: Mid-test

• Handout: Trigonometry Mid-Term Exam

• Assignment: Trigonometry Mid-Term Exam

1. Inverse Trig Functions

Review: Basic Inverse Trig Functions:

• Handout: Inverse Review Worksheet

• Assignment: Inverse Review

Graphs of Inverse Trig Functions:

• Handout: Inverse Trig Graphs Worksheet

• Assignment: Inverse Trig Graphs

Inverse Trig Properties:

• Handout: Inverse Trig Properties Worksheet

• Assignment: Inverse Trig Properties

Area of Triangles:

• Handout: Area of Triangles Worksheet

• Assignment: Area of Triangles

1. Vectors

Introduction to Vectors:

• Handout: Introduction to Vectors Worksheet

• Assignment: Introduction to Vectors

• Handout: Geometric Vectors

• Assignment: Geometric Vectors

Algebraic Vectors:

• Handout: Algebraic Vectors Worksheet

• Assignment: Algebraic Vectors

1. The Polar System

Polar Coordinates:

• Handout: Polar Coordinates Worksheet

• Assignment: Polar Coordinates

Graphing Polar Equations:

• Handout: Graphing Polar Equations Worksheet

• Assignment: Graphing Polar Equations

Polar & Rectangular Coordinates:

• Handout: Converting Polar & Rectangular Equations Worksheet

• Worksheet: Converting Polar & Rectangular Coordinates

• Assignment: Converting Polar & Rectangular Equations

Complex Numbers:

• Handout: Operations With Complex Numbers Worksheet

• Assignment: Operations With Complex Numbers

Polar Form of Complex Numbers:

• Handout: Polar Form of Complex Numbers Worksheet

• Assignment: Polar Form of Complex Numbers

Complex Numbers in Polar Form: Products & Quotients:

• Handout: Products & Quotients Worksheet

• Assignment: Products & Quotients

De Moivre’s Theorem:

• Handout: De Moivre’s Theorem Worksheet

• Assignment: De Moivre’s Theorem

1. Final Exam

Post-Test:

• Assignment: Post-Test

• Handout: Trigonometry Final Exam

• Assignment: Final Exam