Math

ArcTan Block

Inverse tangent (arc tangent) function: y = atan(u)

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# ArcTan Block Documentation

Overview

The ArcTan (inverse tangent) block computes the angle whose tangent equals the input.

Inputs

Input: Any numeric signal

Outputs

atan(x): The inverse tangent (arctangent) in radians, range (-π/2, π/2)

Parameters

None

Mathematical Definition

y(t) = arctan(u(t)) = atan(u(t))

Where: u ∈ ℝ (all reals), y ∈ (-π/2, π/2)

Behavior

Input range: All real numbers
Output range: (-π/2, π/2) ≈ (-1.571, 1.571)
Monotonic increasing function
S-shaped saturation near ±∞

Examples

Example 1: Basic Inverse Tangent

Input: 0 → Output: 0
Input: 1 → Output: π/4 ≈ 0.785
Input: ∞ → Output: π/2 ≈ 1.571
Input: -∞ → Output: -π/2 ≈ -1.571

Example 2: Slope-to-Angle Conversion

Slope (rise/run) → ArcTan → Angle (radians)
Useful for incline measurements

Common Use Cases

1. Slope-to-angle conversion: Convert rise/run to angle 2. Phase unwrapping: Alternative to atan2 for 2-quadrant angles 3. Feedback saturation: Natural saturation limiting signal to ±π/2 4. Nonlinear gain: Smooth nonlinear gain function

Comparison with ArcSin and ArcCos

ArcTan: Works with any input, output ∈ (-π/2, π/2)
ArcSin: Input must be [-1, 1], output ∈ [-π/2, π/2]
ArcCos: Input must be [-1, 1], output ∈ [0, π]
ArcTan2 (future): Use for full angle recovery [0, 2π] from (y,x) pairs

Full Angle Recovery

For recovering angles in the full range [0, 2π], use ArcTan2 (future block) instead:

(x, y) → ArcTan2 → θ ∈ [0, 2π]