Trigonometry Calculator

This calculator computes all six trig functions — sin, cos, tan, sec, csc, cot — from an angle, or finds the angle from inverse functions such as arcsin, arccos, and arctan. It works in both degrees and radians.

Key values: sin 0° = 0, sin 30° = 0.5, sin 45° ≈ 0.707, sin 60° ≈ 0.866, sin 90° = 1. cos 0° = 1, cos 30° ≈ 0.866, cos 60° = 0.5, cos 90° = 0. tan 45° = 1, tan 30° ≈ 0.577, tan 60° ≈ 1.732. tan 90° is undefined.

Use arcsin, arccos, or arctan with a known ratio. Example: sin α = 0.5 → α = arcsin(0.5) = 30°. Example: cos α = 0.5 → α = arccos(0.5) = 60°. Example: tan α = 1 → α = arctan(1) = 45°. Arcsin and arccos return values in [0°, 90°]; arctan returns (−90°, 90°).

Direct: y = sin(α), y = cos(α), y = tan(α) = sin/cos, y = cot(α) = cos/sin, y = sec(α) = 1/cos, y = csc(α) = 1/sin. Inverse: α = arcsin(y), α = arccos(y), α = arctan(y).

Use π = 3.14159.... Convert degrees → radians: rad = degrees × π / 180. Convert radians → degrees: degrees = rad × 180 / π. Key conversions: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.

The fundamental identity is sin²(α) + cos²(α) = 1 for any angle. Derived identities: 1 + tan²(α) = sec²(α) and 1 + cot²(α) = csc²(α). Example check: sin 30° = 0.5, cos 30° ≈ 0.866 → 0.5² + 0.866² = 0.25 + 0.75 = 1 ✓.

Trigonometry is used in construction for roof pitch and ramps, navigation for bearings, physics for vectors and waves, engineering for signals and oscillations, architecture for heights and distances, and computer graphics for rotations and transformations.

Common conversions: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 120° = 2π/3, 135° = 3π/4, 150° = 5π/6, 180° = π, 270° = 3π/2, 360° = 2π.