Fundamentals of Trigonometry – Part 1

About Course

This course, Fundamentals of Trigonometry – Part 1, is designed to build a deep and intuitive understanding of the foundational concepts in trigonometry. From angle measures and unit circle definitions to identities and graphing, this course lays the groundwork for success in Pre-Calculus, Calculus, and beyond. Students will explore the connections between right triangle ratios, circular functions, and graphical representations while mastering the language and logic of trigonometric reasoning. With a focus on visual understanding, procedural fluency, and strategic application, this course is ideal for high school or early college students preparing for advanced math or standardized exams.

Develop a strong conceptual and procedural foundation in trigonometry
Measure and convert angles in degrees and radians
Use the unit circle to evaluate and understand trig functions
Master graphing techniques for sine, cosine, tangent, and reciprocal functions
Evaluate and interpret inverse trig functions and their graphs
Apply and verify key trigonometric identities
Strengthen problem-solving strategies for standardized exams and future math courses
Build fluency in algebraic manipulation involving trig expressions
Gain confidence in approaching complex trig topics with clarity and structure
Prepare for higher-level courses like Pre-Calculus, Calculus, and Physics

Course Content

1. Angles and Radian Measure
This topic introduces the basic language of trigonometry—angles, their measurement in degrees and radians, and key calculations involving arc length and sector area. Students will also learn how to manipulate and interpret angles on the coordinate plane.

1.1 Angle Types and Terminology
1.2 Radian Measure and Conversions
1.3 Arc Length and Sector Area
1.4 Coterminal and Reference Angles

2. Trigonometric Functions and the Unit Circle
This topic connects right triangle definitions of trig functions to the unit circle, empowering students to evaluate trig values for common angles and understand the function behavior across quadrants.

3. Graphs of Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

4. Inverse Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

5. Identities
This topic equips students with the essential toolkit of trigonometric identities—key to simplifying expressions, verifying equalities, and solving equations.

About Course

What Will You Learn?

Course Content

1. Angles and Radian Measure
This topic introduces the basic language of trigonometry—angles, their measurement in degrees and radians, and key calculations involving arc length and sector area. Students will also learn how to manipulate and interpret angles on the coordinate plane.

1.1 Angle Types and Terminology

1.2 Radian Measure and Conversions

1.3 Arc Length and Sector Area

1.4 Coterminal and Reference Angles

2. Trigonometric Functions and the Unit Circle
This topic connects right triangle definitions of trig functions to the unit circle, empowering students to evaluate trig values for common angles and understand the function behavior across quadrants.

2.1 Trig Ratios in Right Triangles

2.2 Unit Circle Definition of Trig Functions

2.3 Evaluating Trig Functions

2.4 Reciprocal and Quotient Identities

3. Graphs of Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

3.1 Graphing Sine and Cosine

3.2 Graphing Tangent and Cotangent

3.3 Graphing Secant and Cosecant

4. Inverse Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

4.1 Understanding Inverse Functions

4.2 Evaluating Inverse Trig Functions

4.3 Graphs of Inverse Trig Functions

5. Identities
This topic equips students with the essential toolkit of trigonometric identities—key to simplifying expressions, verifying equalities, and solving equations.

5.1 Fundamental and Pythagorean Identities

5.2 Co-function and Even-Odd Identities

5.3 Sum and Difference Formulas

5.4 Double-Angle and Half-Angle Formulas

5.5 Product-to-Sum and Sum-to-Product

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Fundamentals of Trigonometry – Part 1

About Course

What Will You Learn?

Course Content

1. Angles and Radian Measure This topic introduces the basic language of trigonometry—angles, their measurement in degrees and radians, and key calculations involving arc length and sector area. Students will also learn how to manipulate and interpret angles on the coordinate plane.

1.1 Angle Types and Terminology

1.2 Radian Measure and Conversions

1.3 Arc Length and Sector Area

1.4 Coterminal and Reference Angles

2. Trigonometric Functions and the Unit Circle This topic connects right triangle definitions of trig functions to the unit circle, empowering students to evaluate trig values for common angles and understand the function behavior across quadrants.

2.1 Trig Ratios in Right Triangles

2.2 Unit Circle Definition of Trig Functions

2.3 Evaluating Trig Functions

2.4 Reciprocal and Quotient Identities

3. Graphs of Trigonometric Functions This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

3.1 Graphing Sine and Cosine

3.2 Graphing Tangent and Cotangent

3.3 Graphing Secant and Cosecant

4. Inverse Trigonometric Functions This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

4.1 Understanding Inverse Functions

4.2 Evaluating Inverse Trig Functions

4.3 Graphs of Inverse Trig Functions

5. Identities This topic equips students with the essential toolkit of trigonometric identities—key to simplifying expressions, verifying equalities, and solving equations.

5.1 Fundamental and Pythagorean Identities

5.2 Co-function and Even-Odd Identities

5.3 Sum and Difference Formulas

5.4 Double-Angle and Half-Angle Formulas

5.5 Product-to-Sum and Sum-to-Product

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1. Angles and Radian Measure
This topic introduces the basic language of trigonometry—angles, their measurement in degrees and radians, and key calculations involving arc length and sector area. Students will also learn how to manipulate and interpret angles on the coordinate plane.

2. Trigonometric Functions and the Unit Circle
This topic connects right triangle definitions of trig functions to the unit circle, empowering students to evaluate trig values for common angles and understand the function behavior across quadrants.

3. Graphs of Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

4. Inverse Trigonometric Functions
This topic brings trigonometric functions to life through graphing. Students will investigate how changes in amplitude, period, and phase affect sine, cosine, and other functions.

5. Identities
This topic equips students with the essential toolkit of trigonometric identities—key to simplifying expressions, verifying equalities, and solving equations.