Inverse Cosine Calculator

The inverse cosine function, commonly written as arccos(x) or cos⁻¹(x), is the inverse of the standard cosine trigonometric function. If you input a value x, the formula solves for angle y such that cos(y) = x. Because trigonometric functions are periodic, the range of the inverse cosine function is strictly restricted to the interval [0, π] radians, or [0°, 180°], to ensure a unique, single-valued output. To convert the resulting radian measure into degrees, the tool multiplies the value by 180 and divides by pi: AngleInDegrees = y * 180 / π.

Let us walk through finding the inverse cosine of x = 0.5. First, we apply the inverse cosine function: y = acos(0.5). In radians, this evaluates to approximately 1.0472. To convert this radian measure into degrees, we multiply by 180 and divide by pi: (1.0472 * 180) / 3.14159, which gives us exactly 60 degrees. Therefore, an input value of 0.5 yields an angle of 60°.

Always verify that your input value for x falls strictly between -1 and 1, as real-valued cosine outputs cannot exceed these boundaries. Pay close attention to whether your application requires output angles in degrees or radians to avoid costly calculation errors in geometry or physics problems. When solving multi-step trigonometric proofs, retain full decimal precision during intermediate steps and only round your final answer.