Trigonometry Calculator

Calculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) plus hyperbolic functions for any angle in degrees, radians or gradians.

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The Six Trigonometric Functions

The three primary functions — sine (sin), cosine (cos) and tangent (tan) — relate angles to ratios of sides in a right triangle. The three reciprocal functions complete the set: cosecant (csc = 1/sin), secant (sec = 1/cos) and cotangent (cot = 1/tan). Remembering SOH-CAH-TOA helps: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

Degrees vs Radians

Degrees divide a circle into 360 parts. Radians measure angles by arc length — a full circle is 2π radians. Radians are the natural unit for calculus and most mathematical formulae. Convert between them: radians = degrees × π/180. Common values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π.

Frequently Asked Questions

These are standard values worth memorising. sin 30° = 0.5, cos 30° = √3/2 ≈ 0.866. cos 60° = 0.5, sin 60° = √3/2 ≈ 0.866. tan 45° = 1 exactly. Also: sin 0° = 0, cos 0° = 1, sin 90° = 1, cos 90° = 0.
Tan = sin/cos. At 90°, cos = 0. Dividing by zero is undefined. On the graph of y = tan(x), there is a vertical asymptote at x = 90° (π/2) — the function approaches +∞ from the left and -∞ from the right.
The unit circle is a circle of radius 1 centred at the origin. For any angle θ, the coordinates of the point on the unit circle are (cos θ, sin θ). This gives an intuitive geometric meaning to sine and cosine values and explains why they range from -1 to 1.
Hyperbolic functions (sinh, cosh, tanh) are analogues of trigonometric functions based on a hyperbola instead of a circle. They appear in engineering (catenary curves, heat distribution), physics (special relativity) and pure mathematics. Unlike sin and cos which are bounded, sinh and cosh grow without limit.
Gradians (also called grades or gon) divide a right angle into 100 parts, making a full circle 400 gradians. They were developed for surveying and are still used in some European geodesy and surveying applications. Most calculators have a GRAD mode alongside DEG and RAD.

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