» Trigonometry Calculator

What does this trigonometry calculator do?
This calculator computes all six trig functions — sin, cos, tan, sec, csc, cot — from an angle, or finds the angle from the inverse functions (arcsin, arccos, arctan, arcsec, arccsc, arccot). Works in both degrees and radians.

What are the values of sin, cos, and tan for common angles?
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.

How do you find an angle using inverse trig functions?
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°).

What are the main trigonometric function formulas?
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).

How do degrees and radians convert?
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.

What is the Pythagorean identity in trigonometry?
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 ✓.

What are common uses of trigonometry in real life?
Trigonometry is used in: construction (roof pitch, ramp angle), navigation (bearing calculations, GPS), physics (resolving force vectors, pendulum motion), engineering (signal processing, oscillations), architecture (calculating heights and distances), and computer graphics (rotations and transformations).

What are common degree to radian conversions?
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.

\begin{align} \pi &= 3.1415926535897...\\ \\ 1\, rad &= \frac {180^{\circ}}{\pi} \approx 57.2957795131^{\circ}\\ \\ \alpha^{\circ} &= \alpha^{rad} \times \frac {180^{\circ}}{\pi}\\ \\ \alpha^{rad} &= \alpha^{\circ} \times \frac {\pi}{180^{\circ}} \end{align}