Trigonometry Basics and Applications

          Module 1: Introduction to Trigonometry

Section 1: What is Trigonometry?
- Lesson 1: Definition and History  
  Module 1, Section 1, Lesson 1 Definition and History
- Lesson 2: Trigonometry in Everyday Life  
  Module 1, Section 1, Lesson 2 Trigonometry in Everyday Life

Section 2: Basic Geometry Review
- Lesson 1: Recap of Angles and Lines  
  Module 1, Section 2, Lesson 1 Recap of Angles and Lines
- Lesson 2: Types of Triangles  
  Module 1, Section 2, Lesson 2 Types of Triangles

Section 3: Understanding Angles
- Lesson 1: Angle Measurement and Tools  
  Module 1, Section 3, Lesson 1 Angle Measurement and Tools
- Lesson 2: Angle Notations (Degrees and Radians)  
  Module 1, Section 3, Lesson 2 Angle Notations (Degrees and Radians)

Section 4: Introduction to Trigonometric Terms
- Lesson 1: Overview of Sine, Cosine, and Tangent  
  Module 1, Section 4, Lesson 1 Overview of Sine, Cosine, and Tangent
- Lesson 2: Understanding Basic Trigonometric Vocabulary  
  Module 1, Section 4, Lesson 2 Understanding Basic Trigonometric Vocabulary

Section 5: Everyday Applications of Trigonometry
- Lesson 1: Real-Life Examples in Navigation and Mapping  
  Module 1, Section 5, Lesson 1 Real-Life Examples in Navigation and Mapping
- Lesson 2: How Trigonometry Helps in Architecture  
  Module 1, Section 5, Lesson 2 How Trigonometry Helps in Architecture

Module 2: Trigonometric Ratios

Section 1: The Sine Function
- Lesson 1: Defining the Sine Ratio in Right Triangles  
  Module 2, Section 1, Lesson 1 Defining the Sine Ratio in Right Triangles
- Lesson 2: Practical Examples Using Sine  
  Module 2, Section 1, Lesson 2 Practical Examples Using Sine

Section 2: The Cosine Function
- Lesson 1: Defining the Cosine Ratio in Right Triangles  
  Module 2, Section 2, Lesson 1 Defining the Cosine Ratio in Right Triangles
- Lesson 2: Practical Use of Cosine in Measurements  
  Module 2, Section 2, Lesson 2 Practical Use of Cosine in Measurements

Section 3: The Tangent Function
- Lesson 1: Defining the Tangent Ratio  
  Module 2, Section 3, Lesson 1 Defining the Tangent Ratio
- Lesson 2: Using Tangent to Solve Right Triangle Problems  
  Module 2, Section 3, Lesson 2 Using Tangent to Solve Right Triangle Problems

Section 4: Solving Missing Sides in Right Triangles
- Lesson 1: Applying Sine and Cosine to Find Lengths  
  Module 2, Section 4, Lesson 1 Applying Sine and Cosine to Find Lengths
- Lesson 2: Using Tangent for Calculating Distances  
  Module 2, Section 4, Lesson 2 Using Tangent for Calculating Distances

Section 5: Pythagorean Relationships and Trigonometry
- Lesson 1: Revisiting the Pythagorean Theorem  
  Module 2, Section 5, Lesson 1 Revisiting the Pythagorean Theorem
- Lesson 2: Connecting the Theorem with Trigonometric Ratios  
  Module 2, Section 5, Lesson 2 Connecting the Theorem with Trigonometric Ratios

Module 3: The Trigonometric Circle

Section 1: Introduction to the Unit Circle
- Lesson 1: What is the Unit Circle?  
  Module 3, Section 1, Lesson 1 What is the Unit Circle?
- Lesson 2: Important Points on the Unit Circle  
  Module 3, Section 1, Lesson 2 Important Points on the Unit Circle

Section 2: Radian Measure
- Lesson 1: Understanding Radians and Their Relationship to Degrees  
  Module 3, Section 2, Lesson 1 Understanding Radians and Their Relationship to Degrees
- Lesson 2: Converting Between Degrees and Radians  
  Module 3, Section 2, Lesson 2 Converting Between Degrees and Radians

Section 3: Sine and Cosine on the Unit Circle
- Lesson 1: Plotting Sine Values Around the Circle  
  Module 3, Section 3, Lesson 1 Plotting Sine Values Around the Circle
- Lesson 2: Plotting Cosine Values on the Unit Circle  
  Module 3, Section 3, Lesson 2 Plotting Cosine Values on the Unit Circle

Section 4: Properties of the Unit Circle
- Lesson 1: Periodicity and Symmetry in Trigonometric Functions  
  Module 3, Section 4, Lesson 1 Periodicity and Symmetry in Trigonometric Functions
- Lesson 2: Identifying Reference Angles  
  Module 3, Section 4, Lesson 2 Identifying Reference Angles

Section 5: Problem Solving with the Unit Circle
- Lesson 1: Finding Angles from Given Sine or Cosine Values  
  Module 3, Section 5, Lesson 1 Finding Angles from Given Sine or Cosine Values
- Lesson 2: Practical Exercises Using the Unit Circle  
  Module 3, Section 5, Lesson 2 Practical Exercises Using the Unit Circle

Module 4: Trigonometric Functions and Graphs

Section 1: Plotting Trigonometric Functions
- Lesson 1: Basics of Graphing Sine and Cosine  
  Module 4, Section 1, Lesson 1 Basics of Graphing Sine and Cosine
- Lesson 2: Introduction to Amplitude and Period  
  Module 4, Section 1, Lesson 2 Introduction to Amplitude and Period

Section 2: Graph Transformations
- Lesson 1: Understanding Phase Shifts in Graphs  
  Module 4, Section 2, Lesson 1 Understanding Phase Shifts in Graphs
- Lesson 2: Exploring Vertical Shifts and Reflections  
  Module 4, Section 2, Lesson 2 Exploring Vertical Shifts and Reflections

Section 3: Hands-on Graphing Activities
- Lesson 1: Plotting Functions Using Graph Paper and Tools  
  Module 4, Section 3, Lesson 1 Plotting Functions Using Graph Paper and Tools
- Lesson 2: Collaborative Graph Analysis  
  Module 4, Section 3, Lesson 2 Collaborative Graph Analysis

Section 4: Introduction to Inverse Trigonometric Functions
- Lesson 1: What Is an Inverse Function?  
  Module 4, Section 4, Lesson 1 What Is an Inverse Function?
- Lesson 2: Basic Ideas of Inverse Sine and Cosine  
  Module 4, Section 4, Lesson 2 Basic Ideas of Inverse Sine and Cosine

Section 5: Exploring Technology in Trigonometry
- Lesson 1: Using Graphing Calculators to Explore Functions  
  Module 4, Section 5, Lesson 1 Using Graphing Calculators to Explore Functions
- Lesson 2: Interactive Software and Simulations for Practice  
  Module 4, Section 5, Lesson 2 Interactive Software and Simulations for Practice

Module 5: Real-World Applications of Trigonometry

Section 1: Trigonometry in Navigation
- Lesson 1: Using Angles and Ratios for Directions  
  Module 5, Section 1, Lesson 1 Using Angles and Ratios for Directions
- Lesson 2: Problem Solving in Map Reading  
  Module 5, Section 1, Lesson 2 Problem Solving in Map Reading

Section 2: Trigonometry in Architecture
- Lesson 1: Measuring Heights and Distances in Structures  
  Module 5, Section 2, Lesson 1 Measuring Heights and Distances in Structures
- Lesson 2: Understanding Structural Design Basics  
  Module 5, Section 2, Lesson 2 Understanding Structural Design Basics

Section 3: Trigonometry in Physics
- Lesson 1: Introduction to Oscillations and Waves  
  Module 5, Section 3, Lesson 1 Introduction to Oscillations and Waves
- Lesson 2: How Trigonometry Explains Periodic Phenomena  
  Module 5, Section 3, Lesson 2 How Trigonometry Explains Periodic Phenomena

Section 4: Trigonometry in Art and Design
- Lesson 1: Applying Angle Concepts to Perspective Drawing  
  Module 5, Section 4, Lesson 1 Applying Angle Concepts to Perspective Drawing
- Lesson 2: Recognizing Patterns and Symmetry in Art  
  Module 5, Section 4, Lesson 2 Recognizing Patterns and Symmetry in Art

Section 5: Capstone Project and Review
- Lesson 1: Planning a Multi-Step Trigonometry Project  
  Module 5, Section 5, Lesson 1 Planning a Multi-Step Trigonometry Project
- Lesson 2: Presenting and Discussing Real-Life Trigonometric Solutions  
  Module 5, Section 5, Lesson 2 Presenting and Discussing Real-Life Trigonometric Solutions