1. What is Tan (3pi/2+A)?

Tan (3pi/2+A) represents the tangent function of the sum of 3π/2 (270 degrees) and angle A. This trigonometric identity demonstrates the periodic nature and phase shifting properties of the tangent function.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( A \) — Angle in radians
• \( \cot \) — Cotangent function (cos/sin)

Explanation: This identity shows that adding 3π/2 to an angle in the tangent function is equivalent to taking the negative cotangent of the original angle.

3. Trigonometric Identity Explanation

Details: The tangent function has a period of π, and adding 3π/2 (which is equivalent to adding π + π/2) results in this specific transformation that relates tangent to cotangent with a sign change.

4. Using the Calculator

Tips: Enter the angle A in radians. The calculator will compute tan(3π/2 + A) using the identity -cot(A). For degrees, convert to radians first (radians = degrees × π/180).

5. Frequently Asked Questions (FAQ)

Q1: Why does tan(3pi/2+A) equal -cot(A)?
A: This is derived from trigonometric identities and the periodic properties of tangent and cotangent functions.

Q2: What is the period of tangent function?
A: The tangent function has a period of π radians (180 degrees), meaning tan(θ + π) = tan(θ).

Q3: How is cotangent related to tangent?
A: Cotangent is the reciprocal of tangent: cot(A) = 1/tan(A) = cos(A)/sin(A).

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

Q5: Are there any restrictions on angle values?
A: Avoid angles where sin(A) = 0, as cot(A) would be undefined (division by zero).