Arcsin Calculator
Calculate the inverse sine (arcsin) of a value.
Graph
Inverse Sine (Arcsin)
The inverse sine function, denoted as arcsin(x) or sin⁻¹(x), is defined as:
\[ \arcsin(x) = \theta \text{ where } \sin(\theta) = x \text{ and } -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} \]
Properties:
- Domain: [-1, 1]
- Range: [-π/2, π/2] radians or [-90°, 90°]
- \(\arcsin(-x) = -\arcsin(x)\)
- \(\arcsin(x) = \frac{\pi}{2} - \arccos(x)\)
- \(\arcsin(x) = \arctan\left(\frac{x}{\sqrt{1-x^2}}\right)\)
Applications:
- Trigonometry
- Physics (wave motion, oscillations)
- Engineering (signal processing)
- Navigation
- Computer graphics
Common Values:
- \(\arcsin(1) = \frac{\pi}{2}\)
- \(\arcsin(0) = 0\)
- \(\arcsin(-1) = -\frac{\pi}{2}\)
- \(\arcsin(\frac{1}{2}) = \frac{\pi}{6}\)
- \(\arcsin(-\frac{1}{2}) = -\frac{\pi}{6}\)