Arctan Calculator Radians To Degrees

Arctan Conversion Formula:

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

Result (θ_deg):

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1. What is Arctan Conversion?

The arctan function (inverse tangent) calculates the angle whose tangent is a given number. This calculator converts the result from radians to degrees, which is more commonly used in many applications.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

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

Where:

\( \theta_{deg} \) — Angle in degrees
\( x \) — Input value (unitless)
\( \pi \) — Mathematical constant Pi (~3.14159)

Explanation: The arctan function returns an angle in radians, which is then converted to degrees by multiplying by 180/π.

3. Importance of Angle Conversion

Details: Degrees are more intuitive for most people and are commonly used in navigation, engineering, and everyday measurements. This conversion is essential when working with trigonometric functions in different contexts.

4. Using the Calculator

Tips: Simply enter any real number value and click calculate. The result will show the angle in degrees whose tangent equals your input value.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of output values?
A: The output will be between -90° and +90° (-π/2 to +π/2 radians).

Q2: How accurate is the calculation?
A: The calculation uses PHP's built-in atan() function which provides high precision, with results rounded to 4 decimal places.

Q3: Can I use this for complex numbers?
A: No, this calculator only handles real number inputs.

Q4: What's the difference between atan and atan2?
A: atan2 takes two arguments (y,x) and returns angles in all four quadrants (-π to π), while atan takes one argument and returns angles only in quadrants I and IV (-π/2 to π/2).

Q5: Why convert to degrees instead of using radians?
A: Degrees are more familiar to most people and are commonly used in many practical applications like navigation and construction.