The Ultimate Trigonometry Course (+FREE Worksheets)

Use these free trigonometry lessons to review angles, right triangles, the unit circle, graphs, identities, and equations. Start with a topic you need, work through its examples, and try its available exercises. This page is a lesson directory; check each lesson for printable practice and answers rather than assuming every link includes a worksheet.

Choose your starting point

If trigonometry is new to you, begin with angle measure and right-triangle ratios, then study the unit circle before graphs, identities, and equations. Review the Pythagorean theorem, similar triangles, basic equation solving, and function notation when they slow you down. You do not need to finish every advanced algebra topic before learning right-triangle trigonometry.

For a class assignment, use your teacher’s syllabus to choose the relevant section. Polar coordinates and complex numbers are useful extensions; the exact scope of a trigonometry or precalculus course varies. OpenStax’s trigonometric-functions chapter offers another public explanation of the core angle, unit-circle, and right-triangle topics.

Free trigonometry lessons by topic

Choose a lesson below. For graph work, connect the equation to amplitude, period, shifts, and domain restrictions. For equations, record the requested interval before finding solutions.

Angles and Measurement

• Degrees and Radians
• Angle Conversions
• Angle Addition and Subtraction Formulas
• Angles of Rotation
• Function Values from the Calculator
• Reference Angles and the Calculator
• Coterminal Angles and Reference Angles
• Arc length and Sector Area

Right Triangle Trigonometry

• Pythagorean Theorem
• Trigonometric Ratios
• Solving Right Triangles
• Special Right Triangles

Trigonometric Functions

• Sine, Cosine, and Tangent
• Reciprocal Functions: Cosecant, Secant, and Cotangent
• Domain and Range of Trigonometric Functions
• Trigonometric Function Values for Key Angles
• The Unit Circle

Trigonometric Identities

• Fundamental Trigonometric Identities
• Pythagorean Trigonometric Identities
• Co-Function, Even-Odd, and Periodicity Identities
• Double Angle Formulas
• Half-Angle Formulas
• Sum and Difference Formulas
• Product-to-Sum and Sum-to-Product Formulas

Inverse Trigonometric Functions

• Definition and Properties
• Applications of Inverse Trigonometric Functions

Solving Trigonometric Equations

• Basic Techniques for Solving Trigonometric Equations
• Factoring and Simplifying Trigonometric Expressions
• Solving Equations with Multiple Angles

Oblique Triangles and the Law of Sines

• Non-Right Triangles
• The Law of Sines
• Ambiguous Case (SSA)
• Applications of the Law of Sines

The Law of Cosines

• Derivation of the Law of Cosines
• Solving Triangles with the Law of Cosines
• Applications of the Law of Cosines

Trigonometric Form of Complex Numbers

• Complex Numbers in Trigonometric Form
• Multiplication and Division of Complex Numbers
• Powers and Roots of Complex Numbers

Polar Coordinates and Graphs

• Introduction to Polar Coordinates
• Converting Between Polar and Rectangular Coordinates
• Graphing Polar Equations
• Applications of Polar Coordinates

Graphs of Trigonometric Functions

• Graph of the Sine Function
• Graph of the Cosine Function
• Amplitude, Period, and Phase Shift
• Writing the Equation of a Sine Graph
• Writing the Equation of a Cosine Graph
• Graph of the Tangent Function
• Graph of the Cosecant Function
• Graph of the Secant Function
• Graph of the Cotangent Function
• Graph of Inverse of the Sine Function
• Graph of Inverse of the Cosine Function
• Graph of Inverse of the Tangent Function
• Sketching Trigonometric Graphs

Practice, check, and correct one skill

Read a worked example, cover the solution, and attempt a similar problem. Use any worksheet or exercises provided on the individual lesson page. Compare your reasoning with the available solution, then retry missed questions without looking. If the lesson does not provide a printable worksheet or answer key, use the examples to identify the skill you need to practise elsewhere.

Why does my calculator give a different result?

Check degree or radian mode first. A straight angle is 180° = π radians. To convert degrees to radians, multiply by π/180; to convert radians to degrees, multiply by 180/π. For example, 60° = π/3 radians.

How do I avoid missing solutions?

A calculator’s inverse function returns a principal value. Use the unit circle, signs in each quadrant, and periodicity to find all solutions on the specified interval. For example, sin x = 1/2 has solutions x = π/6 and 5π/6 on 0 ≤ x < 2π.

Check a trigonometry book and its preview

If you want an additional book alongside these free lessons, open Trigonometry for Beginners and use its public preview to compare the contents with your course. Check the product page’s current format, price, delivery information, and separate Amazon listing before choosing a purchase path.

When you are ready for further study, use the calculus lesson directory. If triangle geometry is the main obstacle, return to the geometry lessons first.