Cos Block

Trigonometric cosine function: y = cos(u)

# Cos Block Documentation

Overview

The Cos block computes the cosine trigonometric function of the input signal.

Inputs

• Input (rad): A numeric signal in radians

Outputs

• cos(x): The cosine of the input, ranging from -1 to 1

Parameters

None

Mathematical Definition

y(t) = cos(u(t))

Behavior

• Input range: Any real number (in radians)
• Output range: [-1, 1]
• The function is continuous and periodic with period 2π

Examples

Example 1: Phase-Shifted Sine

Cosine is sine shifted by π/2:

• Input: 0 → Output: 1
• Input: π/2 → Output: 0
• Input: π → Output: -1
• Input: 3π/2 → Output: 0
• Input: 2π → Output: 1

Example 2: Create Orthogonal Signals

Ramp → Gain(2π) → {Sin, Cos} → Combine
Creates 90° phase-shifted pair for quadrature encoding

Common Use Cases

1. Quadrature signals: Create 90° phase-shifted pairs 2. Frequency conversion: Complex exponential (e^jθ = cos(θ) + j·sin(θ)) 3. Coordinate transforms: Rotation matrices, Clarke/Park transforms 4. Phase detection: Phase-locked loops

See Also

• Sin - Sine function
• Tan - Tangent function
• ArcCos - Inverse cosine