1. What is Tan (pi+A)?

Tan (pi+A) is the value of the trigonometric tangent function of the sum of pi (180 degrees) and the given angle A. This represents a phase shift of angle A by pi radians in the trigonometric circle.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( A \) — Input angle in radians
• \( \tan \) — Tangent trigonometric function

Explanation: This identity shows that adding π radians to an angle does not change the value of its tangent function due to the periodic nature of the tangent function with period π.

3. Trigonometric Identity Explanation

Details: The tangent function has a period of π radians, meaning tan(θ + π) = tan(θ) for all values of θ. This property arises from the fact that both sine and cosine functions change sign when shifted by π, and since tan = sin/cos, the ratio remains unchanged.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why does tan(π + A) equal tan(A)?
A: Because the tangent function is periodic with period π, meaning it repeats its values every π radians.

Q2: What is the period of the tangent function?
A: The tangent function has a period of π radians (180 degrees), unlike sine and cosine which have periods of 2π radians.

Q3: Does this identity work for all angle values?
A: Yes, this identity holds for all real values of A, except when tan(A) is undefined (when A = π/2 + kπ, where k is an integer).

Q4: How is this identity useful in trigonometry?
A: This identity simplifies trigonometric expressions and equations by allowing us to reduce angles larger than π to equivalent angles within the fundamental period.

Q5: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians using the formula: radians = degrees × π/180.