Trigonometry Calculator

Pick a function (sin, cos, tan, asin, acos, atan), enter an angle (degrees or radians) or a ratio, and read the result. A small unit-circle diagram shows where the input angle lives, which helps catch sign mistakes around 90° and 270°.

Good for homework, surveying calculations, and the rare moments in app code when you actually need a trig function and your calculator is across the room. Computes in IEEE 754 double precision, so results match what your programming language would return.

For inverse functions (asin, acos, atan), the principal range is annotated next to each result so you remember which quadrant the answer lives in. atan2 is included separately for cases where you need full quadrant disambiguation.

The six functions: sine, cosine, tangent, and their inverses arcsine, arccosine, arctangent. sin and cos are periodic with period 2π; tan has period π and singularities at π/2 + nπ. The inverse functions return values in restricted principal ranges so they're well-defined functions: arcsin returns [-π/2, π/2], arccos returns [0, π], arctan returns (-π/2, π/2). For full quadrant disambiguation, use atan2(y, x), which returns (-π, π].

Worked example. Compute sin(30°). The tool converts to radians (30° = π/6 ≈ 0.5236 rad) and returns 0.5 — exact for this special angle. cos(30°) = sqrt(3)/2 ≈ 0.8660. tan(30°) = sin(30°)/cos(30°) = 1/sqrt(3) ≈ 0.5774. For an inverse: arcsin(0.7) returns 0.7754 rad ≈ 44.43°. Note that arcsin(sin(180°)) returns 0°, not 180° — because the principal range only covers ±90°. The unit-circle diagram alongside each result shows which quadrant the principal-value answer lives in.

Degrees vs radians: a constant source of bugs in numerical code. Most programming languages' math libraries (JavaScript Math, Python math, C math.h) work in radians. If you're translating a textbook formula in degrees, multiply by π/180 first. The tool shows both unit conventions side by side, plus the equivalent in gradians (used in surveying, where 400 grad = 360°). Pick your input unit deliberately; the output will follow.

The atan2 function is the safe way to recover an angle from (x, y) coordinates. atan(y/x) loses the quadrant — atan(1/1) and atan(-1/-1) both return π/4, even though the first is in quadrant I and the second in quadrant III. atan2(y, x) returns the correct angle for the actual quadrant. Use atan2 in code that turns coordinates into headings, polar coordinates, or angles between vectors. Use atan only when you know x is positive.

Floating-point precision: trig functions compute via Taylor series or CORDIC iteration. The result is accurate to about 15 decimal places in double precision, with one caveat: arguments like 10^10 radians lose precision because most of the bits get consumed by the magnitude, leaving few for the fractional part of the sine wave. For very large arguments, reduce modulo 2π first; the tool warns when this matters.