TI Trig Introduction

This course provides a foundational understanding of trigonometry, empowering students with the tools and confidence to approach real-world applications. From mastering angles to graphing trigonometric functions and exploring practical uses, students will develop essential math skills while fostering curiosity and engagement.

Unit 1: Understanding Angles and Their Measurement

Unit 2: Introduction to Trigonometric Ratios

Unit 3: The Unit Circle

Unit 4: Trigonometric Graphs

Unit 5: Real-Life Applications of Trigonometry

T1 Unit Circle

The Unit Circle: Mastering Trigonometry

Course Summary:

This course provides a comprehensive exploration of the unit circle, a foundational concept in trigonometry. Students will learn to understand its structure, calculate coordinates for special angles, connect trigonometric functions to the unit circle, and apply these concepts to real-world problems. The course also introduces general trigonometric functions to deepen understanding and prepare for advanced topics.

Course Units:

  1. Introduction to the Unit Circle

    • Understand the unit circle’s definition, structure, and significance in trigonometry.

  2. Special Angles and Their Coordinates

    • Explore key angles (e.g., 0 to the power of ring operator comma 3 0 to the power of ring operator comma 4 5 to the power of ring operator comma 6 0 to the power of ring operator comma 9 0 to the power of ring operator) and their corresponding coordinates on the unit circle.

  3. Trigonometric Functions and the Unit Circle

    • Connect sine, cosine, and tangent to points on the unit circle and learn how to use these functions to solve problems.

  4. Applications

    • Apply unit circle concepts to solve real-world problems, including oscillations, rotations, and periodic phenomena.

  5. General Trigonometric Functions

    • Extend knowledge to general trigonometric functions and their graphs, covering periodicity and amplitude.

This course offers a step-by-step approach to mastering the unit circle, making trigonometry accessible and practical for students. Enroll now to begin your trigonometric journey!

T4b Advanced Trigonometric Functions

This course delves into the advanced applications and concepts of trigonometric functions, building upon foundational knowledge. Students will explore complex identities, real-world applications, and advanced mathematical tools, gaining the skills to solve intricate problems and model natural phenomena. The course is structured into five comprehensive units:

  1. Advanced Trigonometric Identities
    Master double-angle, half-angle, sum-to-product, and product-to-sum identities for simplifying expressions and solving complex equations.

  2. Polar Coordinates and Trigonometric Functions
    Explore the relationship between trigonometric functions and polar coordinates, graph polar equations, and apply Euler's formula to complex numbers.

  3. Parametric Equations and Trigonometry
    Analyze motion and curves through parametric equations, focusing on applications like circular motion and projectile paths.

  4. Fourier Series and Harmonic Motion
    Discover how trigonometric functions model periodic phenomena, including sound waves, signal processing, and harmonic motion.

  5. Advanced Applications in Science and Engineering
    Apply trigonometric concepts to solve real-world problems in physics, engineering, and wave phenomena, including light diffraction and wave interference.

This course is ideal for students aiming to deepen their understanding of trigonometry and its applications in advanced mathematics and scientific disciplines.


T3 Trig Equations and Identities

Welcome to the Trigonometry: Equations and Identities course on Young Education (YE). This course explores the fascinating world of trigonometric equations, identities, and their real-world applications. Designed to enhance your mathematical understanding and problem-solving skills, it covers five engaging and interconnected units:

Unit 1: Fundamentals of Trigonometric Equations

In this unit, you will learn the basics of solving trigonometric equations, understand their graphical interpretations, and explore the relationships between angles and trigonometric functions. The foundations built here will prepare you for tackling more advanced concepts.

Unit 2: Trigonometric Identities – Basics

This unit introduces key trigonometric identities, such as Pythagorean, reciprocal, and quotient identities. Through interactive examples, you will develop the skills needed to simplify expressions and prove basic trigonometric relationships.

Unit 3: Advanced Trigonometric Identities

Dive deeper into trigonometry with advanced identities, including sum/difference, double-angle, and half-angle formulas. You will learn to manipulate these identities to solve complex equations and simplify challenging expressions.

Unit 4: Solving Trigonometric Equations with Identities

This unit combines the skills from previous units to tackle trigonometric equations using identities. You will solve problems requiring substitution, factorization, and transformations, preparing you for applications in science, engineering, and beyond.

Unit 5: Real-World Applications of Trigonometric Equations and Identities

In the final unit, explore how trigonometric equations and identities model real-world phenomena, such as sound waves, tidal patterns, and pendulum motion. You will apply your knowledge to practical problems, bringing math to life.

What You'll Gain

By the end of this course, you will:

  • Master the art of solving and graphing trigonometric equations.
  • Build confidence in proving and applying trigonometric identities.
  • Understand the real-world significance of trigonometry in technology, physics, and engineering.