Arcsin Calculator (Inverse Sine)

The arcsin function, formally written as arcsin(x) or sin⁻¹(x), is the inverse of the standard sine function. If you have a value x, the arcsin operation finds the angle y such that sin(y) = x. Because the sine function oscillates infinitely, the range of the arcsin function is strictly restricted to the principal interval of [-π/2, π/2] radians (or -90° to 90°) to ensure a unique, predictable output. The input x must always fall within the domain of [-1, 1], as the sine of any real angle can never exceed these boundaries.

Let us walk through finding the arcsin of a standard trigonometric value. Suppose you want to evaluate arcsin(0.5). First, identify that you are looking for an angle whose sine is equal to 0.5. Looking at the unit circle or standard reference triangles, the angle in the first quadrant whose sine equals 1/2 is π/6 radians, which is equivalent to 30 degrees. Therefore, evaluating y = asin(0.5) yields approximately 0.5236 radians or exactly 30°.

Always verify that your input value is between -1 and 1 inclusive, as numbers outside this range will yield undefined results in real number mathematics. Pay close attention to whether your application requires outputs in degrees or radians to avoid conversion errors in downstream calculations. When writing out inverse trigonometric functions, be careful not to confuse the exponent notation sin⁻¹(x) with a reciprocal exponent; it denotes the inverse function, not 1 divided by sin(x).