Trigonometry Calculator

📋 How to use this calculator

1. Select input unit: degrees (0-360°) or radians (0-2π).
2. Enter the angle value, for example: 30, 45, 90, or pi/4 (the calculator parses pi automatically).
3. Select a function: sin, cos, tan, csc, sec, cot, or inverse (arcsin, arccos, arctan).
4. Press Calculate for the numeric result plus exact values for special angles (30°, 45°, 60°, etc.).
5. View the SVG unit-circle visualization showing the angle position, coordinates (cos θ, sin θ), and quadrant.
6. Check the table of 19 trigonometric identities for Pythagorean, double-angle, sum-angle, and half-angle formulas.
7. Tip: For quick conversion, 1 rad = 57.2958° or π rad = 180°; use degrees for geometry/surveying, radians for calculus/physics.

🧮 Trigonometric Functions & Pythagorean Identities

• Unit circle: x = cos θ, y = sin θ for a point at radius 1
• csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
• Special angles: sin 30°=1/2, sin 45°=√2/2, sin 60°=√3/2
• Double angle: sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ - sin²θ
• Sum angle: sin(A+B) = sin A cos B + cos A sin B

The domain of tan θ is undefined at θ = 90° + 180°k (where cos θ = 0).

💡 Worked example: Calculate sin, cos, tan for θ = 60°

Result: sin 60° = √3/2 ≈ 0.866; cos 60° = 0.5; tan 60° = √3 ≈ 1.732.

❓ Frequently asked questions

📚 Sources & references

• Trigonometry Basics — Khan Academy
• Trigonometric Functions — Wolfram MathWorld
• Precalculus - OpenStax — OpenStax (Rice University)