Arctan Calculator

Calculate the inverse tangent (arctan) of any real number.

Calculator

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Concept

What is Arctan?

The arctan function (also known as inverse tangent) is the inverse of the tangent function. It takes any real number and returns the angle whose tangent is that value.

Definition:
If y = tan(θ), then θ = arctan(y)
Formula

Arctan Formula

The arctan function can be calculated using the following formula:

Formula:
arctan(x) = θ where -∞ < x < ∞ and -90° < θ < 90° (or -π/2 < θ < π/2 in radians)
Values

Common Arctan Values

Special Values

  • arctan(0) = 0°
  • arctan(0.5774) = 30°
  • arctan(1) = 45°
  • arctan(1.7321) = 60°
  • arctan(∞) = 90°
  • arctan(-∞) = -90°

Properties

  • Domain: (-∞, ∞)
  • Range: (-90°, 90°) or (-π/2, π/2)
  • arctan(-x) = -arctan(x)
  • arctan(tan(θ)) = θ for -90° < θ < 90°
Applications

Applications of Arctan

Physics Projectile Motion

Arctan is used to calculate launch angles and trajectories in projectile motion.

Engineering Control Systems

Arctan functions are used in control systems to calculate phase angles and system responses.

Navigation GPS and Location

Arctan is used in GPS systems to calculate bearings and directions.

Tools

Trigonometry Calculators

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