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

Geometric Vectors: Adding & Subtracting:

  • 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

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