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Arctan Calculator

Arctan Formula:

\[ \theta = \arctan(x) \]

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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 a given number. The range of arctan is from -π/2 to π/2 radians (-90° to 90°).

2. How Does the Calculator Work?

The calculator uses the arctan function:

\[ \theta = \arctan(x) \]

Where:

Explanation: The calculator first computes the arctangent in radians, then converts to degrees if requested.

3. Applications of Arctan

Details: Arctan is widely used in mathematics, physics, engineering, and computer graphics. Common applications include calculating angles in right triangles, determining phase angles in signal processing, and computing camera angles in 3D graphics.

4. Using the Calculator

Tips: Enter any real number as input. The calculator will return the angle in either degrees or radians based on your selection.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 units, while radians use 2π (about 6.283) units. Radians are often preferred in mathematical calculations.

Q2: What is the range of arctan?
A: Arctan returns values between -90° and 90° (-π/2 to π/2 radians).

Q3: How is arctan different from arctan2?
A: Arctan2 takes two arguments (y, x) and returns an angle in the correct quadrant, with range -π to π radians (-180° to 180°).

Q4: Can I calculate arctan for complex numbers?
A: This calculator only handles real numbers. Complex arctan requires more advanced mathematics.

Q5: Why does arctan(1) equal 45°?
A: Because tan(45°) = 1, so arctan(1) must be 45°.

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