Trigonometry Applications

          Module 1: Fundamental Concepts in Trigonometry

Section 1: Angles and Triangles
Lesson 1: Understanding Angles  
  Module 1, Section 1, Lesson 1: Understanding Angles
Lesson 2: Properties of Triangles  
  Module 1, Section 1, Lesson 2: Properties of Triangles

Section 2: Trigonometric Ratios
Lesson 1: Defining Sine, Cosine, and Tangent  
  Module 1, Section 2, Lesson 1: Defining Sine, Cosine, and Tangent
Lesson 2: Ratios in Right Triangles  
  Module 1, Section 2, Lesson 2: Ratios in Right Triangles

Section 3: The Unit Circle and Angle Measures
Lesson 1: Introduction to the Unit Circle  
  Module 1, Section 3, Lesson 1: Introduction to the Unit Circle
Lesson 2: Degrees and Radians  
  Module 1, Section 3, Lesson 2: Degrees and Radians

Section 4: Graphing Basic Trigonometric Functions
Lesson 1: Graphing the Sine Function  
  Module 1, Section 4, Lesson 1: Graphing the Sine Function
Lesson 2: Graphing the Cosine Function  
  Module 1, Section 4, Lesson 2: Graphing the Cosine Function

Section 5: Everyday Applications of Basic Trigonometry
Lesson 1: Introduction to Trigonometric Applications  
  Module 1, Section 5, Lesson 1: Introduction to Trigonometric Applications
Lesson 2: Using Angles in Real Life  
  Module 1, Section 5, Lesson 2: Using Angles in Real Life


Module 2: Exploring Trigonometric Functions

Section 1: The Sine Function in Depth
Lesson 1: Sine Function Properties  
  Module 2, Section 1, Lesson 1: Sine Function Properties
Lesson 2: Amplitude and Period of Sine  
  Module 2, Section 1, Lesson 2: Amplitude and Period of Sine

Section 2: The Cosine Function in Depth
Lesson 1: Cosine Function Properties  
  Module 2, Section 2, Lesson 1: Cosine Function Properties
Lesson 2: Amplitude and Period of Cosine  
  Module 2, Section 2, Lesson 2: Amplitude and Period of Cosine

Section 3: The Tangent Function in Depth
Lesson 1: Tangent Function Properties  
  Module 2, Section 3, Lesson 1: Tangent Function Properties
Lesson 2: Graphing and Interpreting Tangent  
  Module 2, Section 3, Lesson 2: Graphing and Interpreting Tangent

Section 4: Relationships among Trigonometric Functions
Lesson 1: Exploring Complementary Relationships  
  Module 2, Section 4, Lesson 1: Exploring Complementary Relationships
Lesson 2: Introduction to the Pythagorean Identity  
  Module 2, Section 4, Lesson 2: Introduction to the Pythagorean Identity

Section 5: Solving Basic Trigonometric Equations
Lesson 1: Techniques for Solving Simple Equations  
  Module 2, Section 5, Lesson 1: Techniques for Solving Simple Equations
Lesson 2: Practical Examples of Trigonometric Equations  
  Module 2, Section 5, Lesson 2: Practical Examples of Trigonometric Equations


Module 3: Inverse Trigonometric Functions

Section 1: Introduction to Inverse Functions
Lesson 1: Understanding Inverse Sine (arcsin)  
  Module 3, Section 1, Lesson 1: Understanding Inverse Sine (arcsin)
Lesson 2: Real-World Context for Inverse Sine  
  Module 3, Section 1, Lesson 2: Real-World Context for Inverse Sine

Section 2: Exploring Inverse Cosine (arccos)
Lesson 1: Understanding Inverse Cosine  
  Module 3, Section 2, Lesson 1: Understanding Inverse Cosine
Lesson 2: Applications of Inverse Cosine  
  Module 3, Section 2, Lesson 2: Applications of Inverse Cosine

Section 3: Exploring Inverse Tangent (arctan)
Lesson 1: Understanding Inverse Tangent  
  Module 3, Section 3, Lesson 1: Understanding Inverse Tangent
Lesson 2: Applications of Inverse Tangent  
  Module 3, Section 3, Lesson 2: Applications of Inverse Tangent

Section 4: Domain and Range of Inverse Functions
Lesson 1: Domain Considerations for Inverses  
  Module 3, Section 4, Lesson 1: Domain Considerations for Inverses
Lesson 2: Range Considerations in Inverse Functions  
  Module 3, Section 4, Lesson 2: Range Considerations in Inverse Functions

Section 5: Problem Solving with Inverse Trigonometry
Lesson 1: Setting Up Equations with Inverses  
  Module 3, Section 5, Lesson 1: Setting Up Equations with Inverses
Lesson 2: Verifying and Interpreting Solutions  
  Module 3, Section 5, Lesson 2: Verifying and Interpreting Solutions


Module 4: Trigonometry in Physics and Engineering Applications

Section 1: Trigonometry in Physics
Lesson 1: The Role of Trigonometry in Physics  
  Module 4, Section 1, Lesson 1: The Role of Trigonometry in Physics
Lesson 2: Resolving Vectors Using Trigonometry  
  Module 4, Section 1, Lesson 2: Resolving Vectors Using Trigonometry

Section 2: Engineering Applications I
Lesson 1: Trigonometry in Construction and Design  
  Module 4, Section 2, Lesson 1: Trigonometry in Construction and Design
Lesson 2: Analyzing Forces with Trigonometry  
  Module 4, Section 2, Lesson 2: Analyzing Forces with Trigonometry

Section 3: Navigation and Surveying
Lesson 1: Using Trigonometry for Navigation  
  Module 4, Section 3, Lesson 1: Using Trigonometry for Navigation
Lesson 2: Basic Surveying Techniques with Trigonometry  
  Module 4, Section 3, Lesson 2: Basic Surveying Techniques with Trigonometry

Section 4: Waves and Oscillations
Lesson 1: Trigonometry in Wave Motion  
  Module 4, Section 4, Lesson 1: Trigonometry in Wave Motion
Lesson 2: Understanding Oscillations and Periods  
  Module 4, Section 4, Lesson 2: Understanding Oscillations and Periods

Section 5: Real-World Problem Solving
Lesson 1: Setting Up Practical Trigonometric Problems  
  Module 4, Section 5, Lesson 1: Setting Up Practical Trigonometric Problems
Lesson 2: Hands-On Techniques for Problem Solving  
  Module 4, Section 5, Lesson 2: Hands-On Techniques for Problem Solving


Module 5: Project-Based Learning and Review

Section 1: Introduction to Trigonometry Projects
Lesson 1: Overview of Trigonometry Projects  
  Module 5, Section 1, Lesson 1: Overview of Trigonometry Projects
Lesson 2: Planning and Organizing a Project  
  Module 5, Section 1, Lesson 2: Planning and Organizing a Project

Section 2: Designing a Trigonometric Model
Lesson 1: Identifying a Real-World Problem  
  Module 5, Section 2, Lesson 1: Identifying a Real-World Problem
Lesson 2: Applying Trigonometric Concepts to Model Building  
  Module 5, Section 2, Lesson 2: Applying Trigonometric Concepts to Model Building

Section 3: Data Collection and Analysis
Lesson 1: Techniques for Data Gathering in Trigonometry  
  Module 5, Section 3, Lesson 1: Techniques for Data Gathering in Trigonometry
Lesson 2: Analyzing and Interpreting Collected Data  
  Module 5, Section 3, Lesson 2: Analyzing and Interpreting Collected Data

Section 4: Presenting Trigonometric Findings
Lesson 1: Creating Effective Presentations  
  Module 5, Section 4, Lesson 1: Creating Effective Presentations
Lesson 2: Communicating Results Clearly  
  Module 5, Section 4, Lesson 2: Communicating Results Clearly

Section 5: Course Review and Final Assessment
Lesson 1: Comprehensive Review of Key Concepts  
  Module 5, Section 5, Lesson 1: Comprehensive Review of Key Concepts
Lesson 2: Final Project Assessment and Reflection  
  Module 5, Section 5, Lesson 2: Final Project Assessment and Reflection