1. What Is Tan (Pi/2+A) Formula?

The formula \(\tan(\pi/2 + A) = -\cot(A)\) is a trigonometric identity that shows the relationship between tangent and cotangent functions when the angle is shifted by \(\pi/2\) radians (90 degrees).

2. How Does The Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( A \) — Angle in radians
• \( \cot(A) \) — Cotangent of angle A, defined as \(\frac{\cos(A)}{\sin(A)}\)

Explanation: This identity demonstrates the phase shift property of trigonometric functions and their relationships through complementary angles.

3. Importance Of Trigonometric Identities

Details: Trigonometric identities like this one are fundamental in mathematics, physics, and engineering for simplifying expressions, solving equations, and analyzing periodic phenomena.

4. Using The Calculator

Tips: Enter the angle value in radians. The calculator will compute the result using the trigonometric identity \(\tan(\pi/2 + A) = -\cot(A)\).

5. Frequently Asked Questions (FAQ)

Q1: Why does tan(pi/2+A) equal -cot(A)?
A: This is derived from the trigonometric identities and the complementary angle relationships between tangent and cotangent functions.

Q2: What is the domain restriction for this formula?
A: The formula is valid for all angles except where sin(A) = 0, as cotangent would be undefined at those points.

Q3: Can I use degrees instead of radians?
A: This calculator uses radians. To convert degrees to radians, multiply by π/180.

Q4: What are practical applications of this identity?
A: This identity is used in signal processing, wave analysis, and solving differential equations involving trigonometric functions.

Q5: How is this related to other trigonometric identities?
A: This is part of a family of shift identities that relate trigonometric functions at complementary angles.