Trigonometry
Overview
Master the relationships between the sides and angles of triangles and the periodic functions that describe them.
Core Concepts Covered
- ✔ Right Triangle Trigonometry (SOHCAHTOA)
- ✔ The Unit Circle and Radian Measure
- ✔ Trigonometric Identities and Equations
- ✔ Law of Sines and Law of Cosines
- ✔ Graphing Periodic Functions (Sine and Cosine Waves)
Interactive Application
Each concept includes clear explanations, step-by-step examples, and guided practice with linked calculators for hands-on reinforcement.
Select a concept or jump directly into a calculator below to begin.
Lessons
Understanding Angles: Degrees and Radians
Learn how we measure rotation using degrees and radians, convert between both systems, and understand why radians are the preferred unit in science and calculus.
Sine, Cosine, and Tangent
Understand the three primary trig functions — what they measure, how to read them from a right triangle, and how to evaluate them at key angles.
Introduction to Sine, Cosine, and Tangent (SOHCAHTOA)
Meet the three primary trigonometric ratios and learn the famous acronym used to remember them for a lifetime.
SOHCAHTOA: Using Trig Ratios to Find Missing Sides
Apply the SOHCAHTOA mnemonic to identify the correct trig ratio for any right triangle problem, set up the equation, and solve for an unknown side.
Solving Right Triangles: Finding Missing Sides
Given any combination of sides and angles, learn to solve a right triangle completely — finding all three sides using the Pythagorean Theorem and trig ratios.
Solving Right Triangles: Finding Missing Angles
Use inverse trig functions — arcsin, arccos, arctan — to find a missing angle when two sides of a right triangle are known.
The Unit Circle
Master the unit circle — the 16 benchmark angles in degrees and radians, their (cos, sin) coordinate pairs, and why this circle is the foundation of all trig beyond right triangles.
The Unit Circle (Foundations)
Explore the bridge between triangles and circles — the unit circle is the secret to understanding trigonometry beyond 90 degrees.
Trig Functions on the Coordinate Plane
Calculate sine, cosine, and tangent for any angle in all four quadrants by using x, y, and r.
Trig Functions on the Coordinate Plane
Extend trigonometry beyond right triangles by defining sin and cos for any angle using a point on the coordinate plane — including angles in all four quadrants.
Graphs of Trig Functions
Understand the shape, period, amplitude, and phase shift of sine and cosine graphs — and learn to sketch and interpret transformed trig functions of the form y = A sin(Bx + C) + D.
Trigonometric Identities
Learn the core trig identities — Pythagorean, reciprocal, and quotient — and use them to simplify expressions and verify equations without plugging in numbers.
Trigonometric Identities (Basics)
Learn the fundamental equations that are always true in trigonometry, used for simplifying complex expressions and solving advanced equations.
Real-World Applications of Trigonometry
Apply everything you’ve learned to solve real problems in navigation, construction, and science.
Real-World Applications of Trigonometry
Apply the Law of Sines, Law of Cosines, and angles of elevation and depression to solve real-world problems involving non-right triangles and navigation.
Calculators
Foundational Trigonometry 3 Foundations Active
Right Triangle Solver
Finds missing sides and angles of a right triangle using Pythagorean theorem.
Tutorial Ready
Trigonometric Functions
Calculate sin, cos, tan, and their reciprocals with exact values.
Tutorial Ready
Unit Circle Explorer
Explore sine, cosine, and tangent values on the unit circle.
Tutorial Ready