Trigonometry Calculator

Whatever unit you type in, the angle is converted to degrees and radians — 360° = 2π rad = 400 grad = 1 turn — and reduced to a coterminal angle in [0°, 360°) to find the quadrant and the reference angle (its acute distance from the x-axis). sin, cos and tan are evaluated in radians; sec, csc and cot are their reciprocals. Where cos θ = 0 the tangent and secant are undefined and the page says so instead of printing 1.6 × 10¹⁶; the same for cot and csc where sin θ = 0. Floating-point dust at the special angles (sin 180° = 1.2 × 10⁻¹⁶) is cleaned to 0.

A value is shown as an exact form when it matches one of the constants of the 30°-60°-90° and 45°-45°-90° triangles to within 10⁻⁹: 0, ±1⁄2, ±√2⁄2, ±√3⁄2, ±1, ±√3, ±√3⁄3, ±2, ±√2, ±2√3⁄3. Angles that are multiples of 30° and 45° (and their coterminal angles) get the full set; other angles get decimals only. The forms are matched numerically, so 0.5 typed as a decimal also reads as 1⁄2.

asin, acos and atan return the principal value in the standard ranges — (−90°, 90°] for asin, acsc, atan and acot, [0°, 180°] for acos and asec — and the input is checked against each function's domain (|x| ≤ 1 for asin and acos, |x| ≥ 1 for asec and acsc). Because the functions repeat, the page also gives the second solution in [0°, 360°) (180° − θ for sine, −θ for cosine, θ + 180° for tangent) and the general solution with a period of 360° or 180°. Calculator conventions: acot 0 = 90°, and acot of a negative value is placed in (90°, 180°) as most tables do. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.