1. What is the Tangent Double Angle Formula?

Definition: This formula calculates the tangent of twice a given angle (2θ) using the tangent of the original angle (θ).

Purpose: It's useful in trigonometry for simplifying expressions and solving problems involving double angles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( θ \) — Original angle (degrees)
• \( \tan(θ) \) — Tangent of the original angle
• \( \tan(2θ) \) — Tangent of the double angle

Explanation: The formula relates the tangent of an angle to the tangent of its double angle through a rational expression.

3. Importance of the Double Angle Formula

Details: This identity is fundamental in trigonometry, used in calculus, physics, engineering, and computer graphics for angle transformations.

4. Using the Calculator

Tips: Enter either the angle in degrees or its tangent value. The calculator will compute tan(2θ). For best results, provide both values.

5. Frequently Asked Questions (FAQ)

Q1: Can I use radians instead of degrees?
A: The formula works with both, but this calculator uses degrees for input. Convert radians to degrees first if needed.

Q2: What happens when tan²(θ) = 1?
A: The denominator becomes zero, making tan(2θ) undefined. This occurs when θ = 45° + k·90° (k ∈ ℤ).

Q3: How accurate are the results?
A: Results are accurate to 6 decimal places, but precision depends on the input values provided.

Q4: Can I calculate tan(θ) from the angle?
A: While this calculator focuses on the double angle formula, tan(θ) = sin(θ)/cos(θ) for any angle θ.

Q5: What are practical applications of this formula?
A: Used in physics for projectile motion, engineering for stress analysis, and computer graphics for rotations.