Trigonometry Formulas

Area of a Triangle (Trigonometric)

Calculate the area of any triangle using A = ½ab·sin(C). Find the area when you know two sides and the included angle.

Double Angle Formulas

Double angle formulas for sin(2θ), cos(2θ), and tan(2θ). Calculate trig functions of double angles with worked examples.

Half Angle Formulas

Half angle formulas for sin(θ/2), cos(θ/2), and tan(θ/2). Calculate trig functions of half angles with worked examples.

Heron's Formula

Calculate the area of any triangle from its three side lengths using Heron's formula: A = √(s(s-a)(s-b)(s-c)). No angles needed.

Inverse Trigonometric Functions

Definitions and ranges for arcsin, arccos, and arctan. Find angles from trig values with inverse trig functions and worked examples.

Law of Cosines

The Law of Cosines c² = a² + b² - 2ab·cos(C) solves any triangle when you know three sides or two sides and the included angle.

Law of Sines

The Law of Sines relates sides and angles of any triangle: a/sin(A) = b/sin(B) = c/sin(C). Solve triangles with step-by-step examples.

Pythagorean Theorem

The Pythagorean theorem a² + b² = c² finds the length of any side of a right triangle. The most famous formula in geometry.

SOHCAHTOA

SOHCAHTOA is the mnemonic for the three basic trig ratios: sin = O/H, cos = A/H, tan = O/A. Essential for solving right triangles.

Trigonometric Identities

Essential trig identities: Pythagorean identities, reciprocal identities, and quotient identities. A complete reference for simplifying trig expressions.

Unit Circle Values

Complete reference for sine, cosine, and tangent values at key angles (0°, 30°, 45°, 60°, 90° and beyond). Essential trig reference table.