Math

ArcSin Block

Inverse sine (arc sine) function: y = asin(u), u ∈ [-1, 1]

Open ArcSin in BlockWerk →

# ArcSin Block Documentation

Overview

The ArcSin (inverse sine) block computes the angle whose sine equals the input.

Inputs

Input [-1, 1]: A numeric signal, range must be [-1, 1]

Outputs

asin(x): The inverse sine (arcsine) in radians, range [-π/2, π/2]

Parameters

None

Mathematical Definition

y(t) = arcsin(u(t)) = asin(u(t))

Where: u ∈ [-1, 1], y ∈ [-π/2, π/2]

Behavior

Input range: [-1, 1] (values outside this range are clamped)
Output range: [-π/2, π/2] ≈ [-1.571, 1.571]
Monotonic increasing function

Examples

Example 1: Basic Inverse Sine

Input: 0 → Output: 0
Input: 1 → Output: π/2 ≈ 1.571
Input: -1 → Output: -π/2 ≈ -1.571
Input: 0.5 → Output: π/6 ≈ 0.524

Example 2: Recovery of Angle from Sine

Ramp (0 to 2π) → Sin → ArcSin → Compare with original
Shows the ambiguity: multiple angles give same sine value

Common Use Cases

1. Angle recovery: Convert sine value back to angle (limited to [-π/2, π/2]) 2. Inverse kinematics: One component of joint angle calculation 3. Calibration: Normalize sensor output to angle 4. Signal conditioning: Scale signals to angle domain

Input Clamping

Values outside [-1, 1] are automatically clamped:

Input > 1 → Clamped to 1 → Output: π/2
Input < -1 → Clamped to -1 → Output: -π/2

Ambiguity Note

ArcSin returns only the principal value in [-π/2, π/2]. For full angle recovery (including [π/2, 3π/2]), use ArcTan2 or ArcCos.