Fundamentals of Trigonometry – Part 2

About Course

Fundamentals of Trigonometry – Part 2 is the continuation of a rigorous and concept-driven exploration of trigonometry, designed to extend students’ understanding beyond the unit circle and right triangle definitions. This course covers the advanced applications of trigonometry in solving equations, modeling with the Laws of Sines and Cosines, and working in polar and parametric forms. Students will also explore the trigonometric representation of complex numbers, culminating in an introduction to Euler’s Formula. Ideal for students progressing toward Pre-Calculus, Calculus, or Physics, this course balances analytical techniques, problem-solving strategies, and graphical intuition to ensure a comprehensive mastery of trigonometric concepts.

Solve a wide variety of trigonometric equations using algebraic and graphical strategies
Apply the Law of Sines and Law of Cosines to solve real-world triangle problems
Calculate the area of any triangle using trigonometric relationships
Represent and operate on complex numbers in polar and trigonometric form
Use De Moivre’s Theorem and Euler’s Formula in mathematical modeling
Graph polar equations and understand symmetry and rotation in polar coordinates
Write and interpret parametric equations to model real-world motion and curves
Deepen understanding of trigonometric identities and their strategic application
Expand into more abstract and advanced mathematical representations
Build readiness for Pre-Calculus, Calculus, and STEM-related applications

Course Content

1. Solving Trigonometric Equations
Students will learn techniques for solving trigonometric equations over specific intervals and in general form, integrating prior knowledge of inverse functions and identities to tackle more advanced problems, including real-world applications.

1.1 Solving Basic Trig Equations
1.2 Using Identities to Solve Equations
1.3 General Solutions and Applications

2. Law of Sines and Law of Cosines
This topic focuses on solving non-right triangles using the Law of Sines and Law of Cosines, addressing different triangle types and situations, including the ambiguous SSA case, and introduces trigonometric formulas for triangle area.

3. Trigonometric Form of Complex Numbers
Students will investigate the polar and trigonometric forms of complex numbers, learning how to perform operations such as multiplication, division, and powers using De Moivre’s Theorem, and explore Euler’s Formula in mathematical modeling.

4. Polar Coordinates and Parametric Equations
This topic introduces alternative coordinate systems and their real-world applications. Students will learn to graph in polar form and represent motion using parametric equations, including modeling projectile motion and circular paths.

About Course

What Will You Learn?

Course Content

1. Solving Trigonometric Equations
Students will learn techniques for solving trigonometric equations over specific intervals and in general form, integrating prior knowledge of inverse functions and identities to tackle more advanced problems, including real-world applications.

1.1 Solving Basic Trig Equations

1.2 Using Identities to Solve Equations

1.3 General Solutions and Applications

2. Law of Sines and Law of Cosines
This topic focuses on solving non-right triangles using the Law of Sines and Law of Cosines, addressing different triangle types and situations, including the ambiguous SSA case, and introduces trigonometric formulas for triangle area.

2.1 Law of Sines

2.2 Law of Cosines

2.3 Area of a Triangle Using Trig

3. Trigonometric Form of Complex Numbers
Students will investigate the polar and trigonometric forms of complex numbers, learning how to perform operations such as multiplication, division, and powers using De Moivre’s Theorem, and explore Euler’s Formula in mathematical modeling.

3.1 Polar Form of Complex Numbers

3.2 Multiplication and Division in Polar Form

3.3 Euler’s Formula and Applications

4. Polar Coordinates and Parametric Equations
This topic introduces alternative coordinate systems and their real-world applications. Students will learn to graph in polar form and represent motion using parametric equations, including modeling projectile motion and circular paths.

4.1 Introduction to Polar Coordinates

4.2 Graphing Polar Equations

4.3 Parametric Equations

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Fundamentals of Trigonometry – Part 2

About Course

What Will You Learn?

Course Content

1. Solving Trigonometric Equations Students will learn techniques for solving trigonometric equations over specific intervals and in general form, integrating prior knowledge of inverse functions and identities to tackle more advanced problems, including real-world applications.

1.1 Solving Basic Trig Equations

1.2 Using Identities to Solve Equations

1.3 General Solutions and Applications

2. Law of Sines and Law of Cosines This topic focuses on solving non-right triangles using the Law of Sines and Law of Cosines, addressing different triangle types and situations, including the ambiguous SSA case, and introduces trigonometric formulas for triangle area.

2.1 Law of Sines

2.2 Law of Cosines

2.3 Area of a Triangle Using Trig

3. Trigonometric Form of Complex Numbers Students will investigate the polar and trigonometric forms of complex numbers, learning how to perform operations such as multiplication, division, and powers using De Moivre’s Theorem, and explore Euler’s Formula in mathematical modeling.

3.1 Polar Form of Complex Numbers

3.2 Multiplication and Division in Polar Form

3.3 Euler’s Formula and Applications

4. Polar Coordinates and Parametric Equations This topic introduces alternative coordinate systems and their real-world applications. Students will learn to graph in polar form and represent motion using parametric equations, including modeling projectile motion and circular paths.

4.1 Introduction to Polar Coordinates

4.2 Graphing Polar Equations

4.3 Parametric Equations

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1. Solving Trigonometric Equations
Students will learn techniques for solving trigonometric equations over specific intervals and in general form, integrating prior knowledge of inverse functions and identities to tackle more advanced problems, including real-world applications.

2. Law of Sines and Law of Cosines
This topic focuses on solving non-right triangles using the Law of Sines and Law of Cosines, addressing different triangle types and situations, including the ambiguous SSA case, and introduces trigonometric formulas for triangle area.

3. Trigonometric Form of Complex Numbers
Students will investigate the polar and trigonometric forms of complex numbers, learning how to perform operations such as multiplication, division, and powers using De Moivre’s Theorem, and explore Euler’s Formula in mathematical modeling.

4. Polar Coordinates and Parametric Equations
This topic introduces alternative coordinate systems and their real-world applications. Students will learn to graph in polar form and represent motion using parametric equations, including modeling projectile motion and circular paths.