Arctan Calculator in Degrees

Arctan Formula:

\[ \theta = \arctan(x) \times \left(\frac{180}{\pi}\right) \]

Result (θ):

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1. What is Arctan?

The arctangent (arctan) is the inverse of the tangent function. It returns the angle whose tangent is the given number. This calculator provides the result in degrees.

2. How Does the Calculator Work?

The calculator uses the arctan formula:

\[ \theta = \arctan(x) \times \left(\frac{180}{\pi}\right) \]

Where:

\( \theta \) — Angle in degrees
\( x \) — Input value (unitless)
\( \pi \) — Mathematical constant (~3.14159)

Explanation: The calculator first computes the arctangent in radians, then converts the result to degrees by multiplying by 180/π.

3. Importance of Arctan Calculation

Details: Arctan is essential in trigonometry, physics, engineering, and computer graphics for determining angles from ratios.

4. Using the Calculator

Tips: Enter any real number as input. The result will be between -90° and +90° (the range of arctan function).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arctan and tan?
A: Tan gives the ratio of sides given an angle, while arctan gives the angle given a ratio (the inverse operation).

Q2: What are common uses of arctan?
A: Calculating angles in right triangles, converting rectangular to polar coordinates, and in various physics applications.

Q3: Why convert to degrees?
A: Degrees are often more intuitive for humans than radians in practical applications.

Q4: What's the range of arctan?
A: The output is always between -90° and +90° (-π/2 to +π/2 radians).

Q5: How accurate is this calculator?
A: It uses PHP's built-in atan() function which provides high precision results.