The Mathematics of Angles and Triangles

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Today, it has applications that are far-reaching, forming the basis of navigation, surveying, engineering, physics, and nearly all fields of science and technology. At its core, trigonometry provides the tools to determine unknown dimensions and angles in geometric figures, a task that is fundamental to countless real-world problems.

This section of our site provides you with powerful tools to solve trigonometric problems, from basic right-angled triangles to complex, non-right (oblique) triangles. We also provide a comprehensive cheat sheet of the most important trigonometric identities and formulas that are essential for students and professionals.

Core Calculators

Right Triangle Calculator - Solve for missing sides and angles of a right-angled triangle.
General Triangle Calculator - Solve any triangle using the laws of sines and cosines.
All-in-One Trigonometry Calculator - An advanced tool with multiple functions, solvers, and graphs.

Frequently Asked Questions

What is SOH CAH TOA?: SOH CAH TOA is a mnemonic device used to remember the three basic trigonometric ratios in a right-angled triangle: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent.
What is the difference between the Law of Sines and the Law of Cosines?: The Law of Sines relates the sides of a triangle to the sines of their opposite angles and is used when you know two angles and any side (ASA or AAS), or two sides and a non-included angle (SSA). The Law of Cosines relates the three sides of a triangle to the cosine of one of its angles and is a generalization of the Pythagorean theorem. It is used when you know two sides and their included angle (SAS) or all three sides (SSS).
What are radians?: Radians are a unit of angle measurement based on the radius of a circle. One radian is the angle at the center of a circle created by an arc equal in length to the radius. A full circle is 2π radians (approximately 6.28 radians), which is equivalent to 360°. Radians are the standard unit of angular measure in all areas of mathematics beyond basic geometry because they simplify many important formulas.
What are inverse trigonometric functions?: Inverse trigonometric functions (like arcsin, arccos, arctan or sin⁻¹, cos⁻¹, tan⁻¹) are used to find an angle when you know the ratio of two sides of a right triangle. For example, if you know sin(θ) = 0.5, then the inverse function tells you that θ = arcsin(0.5) = 30°.