1. What is Arctangent?

The arctangent (atan or tan⁻¹) is the inverse of the tangent function. It returns the angle whose tangent is the given number. The output is typically in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( y \) — Vertical component
• \( x \) — Horizontal component
• \( \theta \) — Resulting angle in radians

Explanation: The function calculates the angle in the right triangle formed by x and y, or the angle of the vector (x,y) from the positive x-axis.

3. Applications of Arctangent

Details: Arctangent is used in trigonometry, physics, engineering, computer graphics, and navigation. It's particularly useful for converting between rectangular and polar coordinates.

4. Using the Calculator

Tips: Enter the y and x values (x ≠ 0). The calculator will output the angle in both radians and degrees. Positive results indicate counter-clockwise angles from the x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2(y,x) considers the signs of both arguments to determine the correct quadrant, while atan(y/x) doesn't distinguish between opposite quadrants.

Q2: What's the range of arctangent?
A: The basic atan function returns values between -π/2 and π/2 radians (-90° to 90°). atan2 returns between -π and π (-180° to 180°).

Q3: How is this different from arcsin or arccos?
A: Each inverse trigonometric function returns angles based on different ratios (sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent).

Q4: What happens when x is zero?
A: When x=0, the tangent is undefined (vertical line). The angle is π/2 (90°) if y>0 or -π/2 (-90°) if y<0.

Q5: How precise are the calculations?
A: The calculator uses PHP's built-in atan() function which provides double-precision floating-point accuracy.