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Trigonometry Calculators

18 Tools

Right triangle solver, Law of Sines and Cosines, and unit circle degree/rad.

Available Trigonometry Calculation Engines

Click any card to open the interactive tool
sin(θ) = Opposite / HypotenuseLaunch
cos(θ) = Adjacent / HypotenuseLaunch
tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)Launch
θ = sin⁻¹(x) where -1 ≤ x ≤ 1Launch
θ = cos⁻¹(x) where -1 ≤ x ≤ 1Launch
θ = tan⁻¹(x) = tan⁻¹(y / x)Launch
sec(θ) = 1 / cos(θ) = Hypotenuse / AdjacentLaunch
csc(θ) = 1 / sin(θ) = Hypotenuse / OppositeLaunch
cot(θ) = 1 / tan(θ) = Adjacent / OppositeLaunch
(x, y) = (cos θ, sin θ) on circle x² + y² = 1Launch
a / sin(A) = b / sin(B) = c / sin(C)Launch
c² = a² + b² - 2ab cos(C)Launch
Solves SSS, SAS, ASA, AAS, and SSA with full metric/imperial length unit supportLaunch
1 rad = 180° / π | 1° = π / 180 radLaunch
sin²(θ) + cos²(θ) = 1 | sin(2θ) = 2 sin(θ) cos(θ)Launch
Solves all inverse trig functions in degrees, radians, and turn fractionsLaunch
x = r cos(θ), y = r sin(θ)Launch
r = √(x² + y²), θ = atan2(y, x)Launch
Computational Standards: Trigonometry Analysis Working Group
Peer-Verified AlgorithmsUpdated: September 2026

Trigonometric Functions, Angular Geometry & Wave Mechanics

Comprehensive theoretical background, mathematical principles, and practical application standards

Trigonometry explores the mathematical relationships between the side lengths and angles of triangles, as well as circular coordinate systems. From periodic sine and cosine wave oscillations in electrical alternating currents to geodesic navigation and surveying, trigonometric principles are foundational.

Key concepts include right-triangle ratios (Sine, Cosine, Tangent), inverse functions (arcsin, arccos, arctan), the unit circle, and the Laws of Sines and Cosines for oblique triangles.

Our trigonometry calculators support dual-mode evaluation in both Degrees (0°–360°) and Radians (0–2π), ensuring consistency for engineering, physics, and pure mathematical modeling.

Key Methodological Principles in Trigonometry

The SOH-CAH-TOA Ratios

In right triangles: sin(θ) = Opposite/Hypotenuse, cos(θ) = Adjacent/Hypotenuse, tan(θ) = Opposite/Adjacent.

Radian vs. Degree Mode Calibration

One radian equals 180/π (~57.2958°). Evaluating calculus and wave mechanics requires radian mode, while architectural surveying uses degrees.

The Law of Cosines

For any triangle: c² = a² + b² - 2ab·cos(C), generalizing the Pythagorean theorem to non-right triangles.

Frequently Asked Questions About Trigonometry

Clear answers to fundamental computation and modeling inquiries

What is the difference between calculating in degrees versus radians?

Degrees divide a complete circle into 360 units, while radians measure angular distance by arc length radius (2π radians in a circle). Choosing the wrong mode causes severe numerical errors.

When should the Law of Cosines be used instead of the Pythagorean theorem?

The Law of Cosines applies to any triangle (acute, obtuse, or right). The Pythagorean theorem applies strictly when the angle between sides is exactly 90°.

What is the tangent of 90 degrees?

The tangent of 90 degrees (or π/2 radians) is undefined because it requires dividing by zero (cos(90°) = 0).