Learn Trigonometry Through Example Problems
Master trigonometry through step-by-step example problems covering angles, right triangle trigonometry, trigonometric functions, the unit circle, identities, graphing, inverse functions, and applications. Build understanding, strengthen problem-solving skills, and prepare for homework, quizzes, and exams.
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 1: Basic Trigonometric Concepts Example Problems
Develop a foundation in angle measurement, radians, arc length, sectors, triangles, and geometric applications using clear, step-by-step examples.
How To Classify Angles: Acute, Right, Obtuse, Straight, And Reflex Examples
How To Convert Between Degrees And Radians
How To Draw Angles in Standard Position
How To Find The Area Of A Sector
How To Find The Angles In A Triangle
How To Solve Shadow Problems Using Similar Triangles
How To Calculate The Radius of a Cone Using Similar Triangles
Chapter 2: Right Triangle Trigonometry Example Problems
Learn how to work with trigonometric functions, reference angles, the unit circle, and right triangles to solve a variety of problems.
Chapter 3: Trigonometric Functions Example Problems
Practice evaluating trigonometric functions, finding exact values, and analyzing points on the coordinate plane.
Chapter 4: Graphs of Trigonometric Functions Example Problems
Learn how to graph sine, cosine, and tangent functions by identifying key features such as amplitude, period, phase shift, and asymptotes.
Chapter 5: Inverse Trigonometric Function Example Problems
Develop confidence evaluating inverse trigonometric functions and solving problems involving restricted domains and exact values.
Chapter 6: Trigonometric Identities Example Problems
Master the use of identities, formulas, and algebraic techniques to simplify expressions, evaluate functions, and verify trigonometric identities.
How to Use the Pythagorean Identity to Find Trigonometric Values
How to Use Periodicity Identities to Simplify Trigonometric Functions
How to Use Even and Odd Identities in Trigonometry
How to Use Sum and Difference Formulas: Sine Example
How to Use Sum and Difference Formulas: Cosine Example
How to Use Sum and Difference Formulas: Tangent Example
How to Use Sum and Difference Formulas for Simplifying Trigonometric Expressions
How to Use Product-to-Sum Identities in Trigonometry
How to Use Sum-to-Product Identities in Trigonometry
How to Use Double Angle Formulas in Trigonometry
How to Use Power Reduction Formulas in Trigonometry
How to Use Half-Angle Formulas in Trigonometry
How to Simplify Trigonometric Expressions: Example 1
How to Simplify Trigonometric Expressions: Example 2
How to Simplify Trigonometric Expressions: Example 3
How to Simplify Trigonometric Expressions: Example 4
How to Simplify Trigonometric Expressions: Example 5
How to Verify Trigonometric Identities: Example 1
How to Verify Trigonometric Identities: Example 2
How to Verify Trigonometric Identities: Example 3
How to Verify Trigonometric Identities: Example 4
How to Verify Trigonometric Identities: Example 5
How to Verify Trigonometric Identities: Example 6
How to Verify Trigonometric Identities: Example 7
How to Verify Trigonometric Identities: Example 8
How to Verify Trigonometric Identities: Example 9
How to Verify Trigonometric Identities: Example 10
How to Verify Trigonometric Identities: Example 11
Chapter 7: Trigonometric Equations Example Problems
Learn systematic methods for solving trigonometric equations using inverse functions, identities, factoring, and algebraic techniques.
How to Solve Trigonometric Equations with a Single Sine Function
How to Solve Trigonometric Equations with a Single Cosine Function
How to Solve Trigonometric Equations With a Single Tangent Function
How to Solve Trigonometric Equations With Multiple Angles (Sine Function)
How to Solve Trigonometric Equations With Multiple Angles (Cosine Function)
How to Solve Trigonometric Equations With Multiple Angles (Tangent Function)
How to Solve Trigonometric Equations Using Factoring | Example 1
How to Solve Trigonometric Equations Using Factoring | Example 2
How to Solve Trigonometric Equations Using Factoring | Example 3
How to Solve Quadratic Trigonometric Equations | Example 1
How to Solve Quadratic Trigonometric Equations | Example 2
How to Solve Quadratic Trigonometric Equations | Example 3
How to Solve Trigonometric Equations Using Identities | Example 1
How to Solve Trigonometric Equations Using Identities | Example 2
How to Solve Trigonometric Equations Using Identities | Example 3
How to Solve Trigonometric Equations Using Identities | Example 4
Chapter 8: Additional Trigonometric Topics Example Problems
Apply trigonometry to oblique triangles, polar coordinates, parametric equations, and complex numbers through detailed worked examples.
Oblique Triangles
How to Solve a Triangle Using the Law of Sines (AAS)
How to Solve a Triangle Using the Law of Sines (ASA)
Law of Sines – Ambiguous Case (SSA) | No Triangle Example
Law of Sines – Ambiguous Case (SSA) | One Right Triangle
Law of Sines – Ambiguous Case (SSA) | One Oblique Triangle
Law of Sines – Ambiguous Case (SSA) | Two Oblique Triangles
Polar Coordinates
How to Convert Polar Coordinates to Rectangular Coordinates
How to Convert Rectangular Coordinates to Polar Coordinates
How to Convert Polar Equations to Rectangular Equations
How to Convert Rectangular Equations to Polar Equations
How to Sketch a Curve from a Parametric Equation | 3 Examples
How to Eliminate the Parameter and Convert to a Rectangular Equation
About Dr. Cheryl Hile
Understand The Math was created by Dr. Cheryl Hile, who earned a Ph.D. in Engineering Science and Applied Mathematics from Northwestern University. She has more than 25 years of experience teaching mathematics at the university level, including 20 years at Penn State. The lessons and guided notes on this site are based on materials she developed for her university courses.