Arctan Calculator Degrees To Radians

Arctan Degrees to Radians Formula:

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

Result (θ_rad):

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1. What is Arctan Degrees to Radians Conversion?

The arctan function (inverse tangent) returns an angle whose tangent is the given number. This calculator converts that angle from degrees to radians, which is often required in mathematical and engineering calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( x \) — Input value (unitless)
\( \arctan(x) \) — Angle in degrees whose tangent is x
\( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The calculator first finds the angle in degrees whose tangent is the input value, then converts that angle to radians.

3. Importance of Angle Conversion

Details: Radians are the standard unit of angular measure in mathematics. Many trigonometric functions and calculus operations require angles to be in radians rather than degrees.

4. Using the Calculator

Tips: Simply enter any real number value. The calculator will compute the arctangent of that value and convert the resulting angle from degrees to radians.

5. Frequently Asked Questions (FAQ)

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

Q2: Why convert degrees to radians?
A: Many mathematical operations, especially in calculus and physics, require angles to be in radians for correct results.

Q3: Can I input very large numbers?
A: Yes, but the result will approach ±π/2 radians (±90°) as the input approaches ±∞.

Q4: How precise are the results?
A: Results are accurate to 6 decimal places, sufficient for most practical applications.

Q5: What's the difference between atan and arctan?
A: They are the same function - both represent the inverse tangent function.