Arcsin Calculator
Calculate inverse sine (arcsine) values in degrees and radians with step-by-step calculations. Perfect for trigonometry, mathematics, and engineering applications.
Inverse Sine Calculator
Common Arcsin Values
Click on these links to see instant calculations with common sine values:
Inverse Sine (Arcsin)
The inverse sine function, denoted as arcsin or sin⁻¹, is the inverse of the sine function. It returns the angle whose sine is the given value, within the principal value range.
Arcsin Properties
Range: [-90°, 90°] or [-π/2, π/2] radians
If sin(θ) = x, then arcsin(x) = θ
arcsin(sin(x)) = x (for x in range)
sin(arcsin(x)) = x (for x in domain)
Common Arcsin Values
| Input Value | Degrees | Radians | Exact Value |
|---|---|---|---|
| -1 | -90° | -π/2 | -π/2 |
| -√3/2 ≈ -0.866 | -60° | -π/3 | -π/3 |
| -√2/2 ≈ -0.707 | -45° | -π/4 | -π/4 |
| -1/2 = -0.5 | -30° | -π/6 | -π/6 |
| 0 | 0° | 0 | 0 |
| 1/2 = 0.5 | 30° | π/6 | π/6 |
| √2/2 ≈ 0.707 | 45° | π/4 | π/4 |
| √3/2 ≈ 0.866 | 60° | π/3 | π/3 |
| 1 | 90° | π/2 | π/2 |
- Trigonometry: Solve inverse trigonometric problems and find angles from ratios
- Engineering: Calculate angles in mechanical and electrical engineering applications
- Physics: Determine angles in wave analysis, optics, and mechanics problems
- Navigation: Calculate bearing angles and directional measurements
- Computer Graphics: Compute rotation angles and vector orientations
Frequently Asked Questions
What is arcsin?
Arcsin (inverse sine) is the inverse function of sine. If sin(θ) = x, then arcsin(x) = θ. It returns the angle whose sine is the given value, with a range of -90° to 90° (or -π/2 to π/2 radians).
What is the domain of arcsin?
The domain of arcsin is [-1, 1], meaning the input value must be between -1 and 1 inclusive. Values outside this range are undefined because sine values cannot exceed this range.
What is the range of arcsin?
The range of arcsin is [-90°, 90°] in degrees or [-π/2, π/2] in radians. This is the principal value range for the inverse sine function.