1. What is Tan(1/x)?

The tan(1/x) function calculates the tangent of the reciprocal of x. This function has interesting behavior as x approaches zero and is used in various mathematical analyses.

2. How Does the Calculator Work?

The calculator computes the trigonometric tangent of the reciprocal of the input value x:

Where:

• \( x \) — Any real number except zero (unitless)
• The result is unitless

Explanation: The function first calculates 1 divided by x, then computes the tangent of that value.

3. Mathematical Properties

Details: The tan(1/x) function oscillates infinitely as x approaches zero. It's undefined at x=0 and has vertical asymptotes at points where 1/x = (n+0.5)π for integer n.

4. Using the Calculator

Tips: Enter any real number except zero. The calculator will return the tangent of the reciprocal of your input value.

5. Frequently Asked Questions (FAQ)

Q1: What happens when x approaches zero?
A: The function oscillates infinitely between -∞ and +∞ as x approaches zero, with the oscillations becoming increasingly rapid.

Q2: What is the domain of tan(1/x)?
A: All real numbers except x=0 and x=1/((n+0.5)π) for any integer n (where the function has vertical asymptotes).

Q3: What are practical applications of tan(1/x)?
A: It's primarily used in mathematical analysis to study function behavior near singularities and in educational contexts to demonstrate complex function behavior.

Q4: How accurate is this calculation?
A: The calculation uses PHP's built-in tan() function which provides high precision, though extremely large or small values may show floating-point limitations.

Q5: Why does the calculator round to 6 decimal places?
A: This provides a balance between precision and readability for most practical purposes.