1. What is the Tan (A/2) Formula?

The formula \(\tan\left(\frac{A}{2}\right) = \frac{1 - \cos A}{\sin A}\) is a half-angle identity in trigonometry that expresses the tangent of half an angle in terms of the sine and cosine of the full angle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \tan\left(\frac{A}{2}\right) \) — Tangent of half angle A
• \( \cos A \) — Cosine of angle A
• \( \sin A \) — Sine of angle A

Explanation: This formula provides a direct way to calculate the tangent of half an angle when you know the sine and cosine of the original angle.

3. Importance of Half-Angle Formulas

Details: Half-angle formulas are essential in trigonometry for simplifying expressions, solving equations, and calculating values that would otherwise be difficult to compute directly.

4. Using the Calculator

Tips: Enter valid values for Sin A and Cos A (between -1 and 1). Note that Sin A cannot be zero as it would result in division by zero.

5. Frequently Asked Questions (FAQ)

Q1: Why can't Sin A be zero?
A: When Sin A is zero, the denominator becomes zero, which results in division by zero - an undefined mathematical operation.

Q2: Are there alternative half-angle formulas?
A: Yes, there are alternative forms such as \(\tan\left(\frac{A}{2}\right) = \frac{\sin A}{1 + \cos A}\) and \(\tan\left(\frac{A}{2}\right) = \frac{1 - \cos A}{\sin A}\).

Q3: What are the domain restrictions?
A: The formula is valid for all angles A except those where Sin A = 0 (i.e., A = nπ, where n is an integer).

Q4: Can this formula be used for any angle?
A: Yes, the formula works for any angle A (in radians or degrees) as long as Sin A ≠ 0.

Q5: How is this formula derived?
A: The formula can be derived from the double-angle formulas and trigonometric identities involving sine and cosine functions.