ArcCos Block

Inverse cosine (arc cosine) function: y = acos(u), u ∈ [-1, 1]

# ArcCos Block Documentation

Overview

The ArcCos (inverse cosine) block computes the angle whose cosine equals the input.

Inputs

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

Outputs

• acos(x): The inverse cosine (arccosine) in radians, range [0, π]

Parameters

None

Mathematical Definition

y(t) = arccos(u(t)) = acos(u(t))

Where: u ∈ [-1, 1], y ∈ [0, π]

Behavior

• Input range: [-1, 1] (values outside are clamped)
• Output range: [0, π] ≈ [0, 3.142]
• Monotonic decreasing function

Examples

Example 1: Basic Inverse Cosine

• Input: 1 → Output: 0
• Input: 0 → Output: π/2 ≈ 1.571
• Input: -1 → Output: π ≈ 3.142

Example 2: Angle from Dot Product

In vector geometry, acos is used to find angle between vectors:

(u · v) / (||u|| ||v||) → ArcCos → Angle between vectors

Common Use Cases

1. Vector angle calculation: Find angle between two vectors 2. Calibration: Convert sensor readings to angles 3. Robotics: Inverse kinematics for certain geometries 4. Signal recovery: Reverse cosine transformations

Input Clamping

Values outside [-1, 1] are automatically clamped to [-1, 1].

Comparison with ArcSin

• ArcSin output range: [-π/2, π/2]
• ArcCos output range: [0, π]
• Relationship: acos(x) + asin(x) = π/2

See Also

• Cos - Cosine function
• ArcSin - Inverse sine
• ArcTan - Inverse tangent