Inverse Sine (Arcsin) Calculator Formula

Understand the math behind the inverse sine (arcsin) calculator. Each variable explained with a worked example.

Use the Inverse Sine (Arcsin) Calculator

Formulas Used

Angle Rad

angle_rad = asin(val)

Angle Deg

angle_deg = asin(val) * 180 / pi

Variables

VariableDescriptionDefault
valValue (-1 to 1)0.5

How It Works

Inverse Sine (Arcsin)

Definition

arcsin(x) = the angle whose sine is x

If sin(angle) = x, then arcsin(x) = angle.

Domain and Range

  • Domain: -1 ≤ x ≤ 1
  • Range: -90° to 90° (-pi/2 to pi/2 radians)

    • Common Values

  • arcsin(0) = 0°
  • arcsin(0.5) = 30°
  • arcsin(√2/2) = 45°
  • arcsin(1) = 90°

    • Worked Example

    Find arcsin(0.5).

    val = 0.5
    1. 01arcsin(0.5) = pi/6 radians
    2. 02= 30 degrees
    3. 03Verification: sin(30°) = 0.5

    Frequently Asked Questions

    What is arcsin?

    Arcsin (inverse sine) returns the angle whose sine equals the given value. It undoes the sine function.

    Why is the range limited to -90° to 90°?

    To make arcsin a proper function (single output), its range is restricted to -90° to 90°. Other angles with the same sine can be found using symmetry.

    What happens if the input is outside -1 to 1?

    Arcsin is only defined for inputs between -1 and 1 in real numbers, since sine never produces values outside this range.

    Ready to run the numbers?

    Open Inverse Sine (Arcsin) Calculator