Arctan Calculator
Calculate the inverse tangent (arctan) of any real number.
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Table of Contents
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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