1. What is Tan (2pi+A) Formula?

The formula tan(2π + A) = tan(A) demonstrates the periodic property of the tangent function. Adding 2π (360 degrees) to any angle A results in the same tangent value, showing that the tangent function has a period of π.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( A \) — Angle in radians
• \( 2\pi \) — 360 degrees or full circle
• \( \tan \) — Tangent trigonometric function

Explanation: The tangent function is periodic with period π, meaning tan(θ + π) = tan(θ). Adding 2π (which is 2 periods) brings the angle back to its original position on the unit circle.

3. Trigonometric Identity Explanation

Details: This identity is fundamental in trigonometry and is based on the circular nature of trigonometric functions. It shows that the tangent function repeats its values every π radians (180 degrees).

4. Using the Calculator

Tips: Enter the angle A in radians. The calculator will compute tan(2π + A) which equals tan(A). For degrees, convert to radians first (degrees × π/180).

5. Frequently Asked Questions (FAQ)

Q1: Why does tan(2π + A) equal tan(A)?
A: Because the tangent function has a period of π, and 2π represents two full periods, bringing the angle back to its original position.

Q2: Does this work for all angles?
A: Yes, this identity holds for all real values of A, except where tan(A) is undefined (at π/2 + kπ, where k is an integer).

Q3: What is the period of tangent function?
A: The tangent function has a period of π radians (180 degrees), unlike sine and cosine which have periods of 2π.

Q4: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180.

Q5: What are practical applications of this identity?
A: This identity is used in solving trigonometric equations, simplifying expressions, and in various engineering and physics applications involving periodic phenomena.