Trigonometry Calculator Calculate all six trig functions (sin, cos, tan, csc, sec, cot) and inverse trig functions.

What Is Trigonometry Calculator?

The Trigonometry Calculator computes all six trigonometric functions for any angle, or finds angles from trigonometric values using inverse functions. In forward mode, enter an angle in degrees or radians to see sin, cos, tan, csc, sec, and cot values. Quick-select buttons for common angles (0°, 30°, 45°, 60°, 90°, 180°) make it easy to reference standard values. In inverse mode, select arcsin, arccos, or arctan, enter a value, and get the angle in both degrees and radians.

Why Use Trigonometry Calculator?

• All six trig functions calculated simultaneously
• Both degrees and radians supported
• Inverse trig functions (arcsin, arccos, arctan)
• Quick-select buttons for common reference angles

Common Use Cases

Math Homework

Calculate trig function values for geometry and calculus problems.

Engineering

Compute angles and distances for structural and mechanical design.

Physics

Solve wave, rotation, and vector decomposition problems.

Navigation

Calculate bearings, distances, and positions using trigonometry.

Technical Guide

The six trigonometric functions of angle θ: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = sin/cos = opposite/adjacent. Reciprocals: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ). Conversion: radians = degrees × π/180. Inverse functions return angles: arcsin(x) = θ where sin(θ) = x (domain: -1 ≤ x ≤ 1, range: -π/2 to π/2). Undefined values: tan(90°) is undefined (cos = 0), csc(0°) is undefined (sin = 0). The Pythagorean identity: sin²(θ) + cos²(θ) = 1.

Tips & Best Practices

• 1
  Remember: sin(30°) = 0.5, cos(60°) = 0.5, tan(45°) = 1
• 2
  Radians are the natural unit in calculus; degrees are more intuitive for everyday use
• 3
  π radians = 180°, so π/6 = 30°, π/4 = 45°, π/3 = 60°
• 4
  Values near 0 or ±1 for sin/cos can indicate special angles (0°, 30°, 45°, 60°, 90°)

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Frequently Asked Questions

Q What is the difference between degrees and radians?

Both measure angles. 360° = 2π radians. Radians are based on the circle's radius: 1 radian ≈ 57.3°. Calculus and most physics formulas use radians.

Q Why is tan(90°) undefined?

Because cos(90°) = 0, and tan = sin/cos. Division by zero is undefined. Graphically, the tangent function has vertical asymptotes at ±90°, ±270°, etc.

Q What are the domains of inverse trig functions?

arcsin and arccos have domain [-1, 1]. arctan has domain (-∞, ∞). These constraints exist because sin and cos never exceed ±1.

Q What is SOH-CAH-TOA?

A mnemonic for right triangles: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

Q Can I use trig functions for non-right triangles?

Yes, using the Law of Sines (a/sinA = b/sinB) and Law of Cosines (c² = a² + b² − 2ab cosC) for any triangle.

About This Tool

Trigonometry Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.