Math

Tan Block

Trigonometric tangent function: y = tan(u)

Open Tan in BlockWerk →

# Tan Block Documentation

Overview

The Tan block computes the tangent trigonometric function of the input signal.

Inputs

Input (rad): A numeric signal in radians

Outputs

tan(x): The tangent of the input

Parameters

None

Mathematical Definition

y(t) = tan(u(t)) = sin(u(t)) / cos(u(t))

Behavior

Input range: Any real number except odd multiples of π/2 (where cos = 0)
Output range: All real numbers (-∞ to +∞)
Function has vertical asymptotes at ±π/2, ±3π/2, etc.
Period: π (not 2π like sin/cos)

Examples

Example 1: Basic Tangent

Input: 0 → Output: 0
Input: π/4 → Output: 1
Input: π/3 → Output: √3 ≈ 1.732
Input: π/2 → Output: undefined (asymptote)

Example 2: Angle-to-Slope Conversion

Tan is useful for converting angles to slopes:

Angle (radians) → Tan → Slope (rise/run)

Common Use Cases

1. Angle-to-slope conversion: Get slope from angle 2. Inverse kinematics: Atan2 for angle from x,y coordinates 3. Signal processing: Nonlinear transformations 4. Feedback control: Tangent as a nonlinear sensor characteristic

Numerical Stability

Caution: Tan has singularities at odd multiples of π/2
Recommendation: Add bounds checking to avoid asymptotes
Use with caution when input angles are not constrained