Arctan Calculator
Calculate the inverse tangent (arctan) of a value.
Graph
Inverse Tangent (Arctan)
The inverse tangent function, denoted as arctan(x) or tan⁻¹(x), is defined as:
\[ \arctan(x) = \theta \text{ where } \tan(\theta) = x \text{ and } -\frac{\pi}{2} < \theta < \frac{\pi}{2} \]
Properties:
- Domain: (-∞, ∞)
- Range: (-π/2, π/2) radians or (-90°, 90°)
- \(\arctan(-x) = -\arctan(x)\)
- \(\arctan(x) = \arcsin\left(\frac{x}{\sqrt{1+x^2}}\right)\)
- \(\arctan(x) = \arccos\left(\frac{1}{\sqrt{1+x^2}}\right)\) for x > 0
Applications:
- Trigonometry
- Physics (projectile motion)
- Engineering (control systems)
- Navigation
- Computer graphics
Common Values:
- \(\arctan(1) = \frac{\pi}{4}\)
- \(\arctan(0) = 0\)
- \(\arctan(-1) = -\frac{\pi}{4}\)
- \(\arctan(\sqrt{3}) = \frac{\pi}{3}\)
- \(\arctan(-\sqrt{3}) = -\frac{\pi}{3}\)