1. What is the Arctan Distance Formula?

The Arctan Distance Formula calculates linear distance from a radius and angle in radians using the arctangent function. It's particularly useful in circular motion problems and angular measurements.

2. How Does the Calculator Work?

The calculator uses the arctan distance formula:

Where:

• \( r \) — Radius in feet
• \( \theta \) — Angle in radians
• \( \arctan \) — Inverse tangent function

Explanation: The formula converts angular measurement (in radians) to linear distance along the circumference.

3. Importance of Distance Calculation

Details: Accurate distance calculation from angular measurements is crucial in engineering, physics, and navigation applications where circular motion or angular displacement is involved.

4. Using the Calculator

Tips: Enter radius in feet and angle in radians. Both values must be positive numbers. The calculator will compute the linear distance equivalent.

5. Frequently Asked Questions (FAQ)

Q1: Why use arctan instead of simple multiplication?
A: Arctan accounts for the non-linear relationship between angle and distance in circular motion, providing more accurate results for larger angles.

Q2: What are typical applications of this calculation?
A: Used in robotics (arm movement), astronomy (angular distances), and mechanical engineering (gear rotations).

Q3: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians first (radians = degrees × π/180).

Q4: What's the maximum angle this works for?
A: The formula works best for angles less than π/2 radians (90 degrees). For larger angles, other trigonometric approaches may be needed.

Q5: How precise is this calculation?
A: Precision depends on input accuracy. The calculator provides results to 4 decimal places.