Find inverse sine angles, exact forms, decimal values, graphs, related trigonometric results, equation solutions, and exportable calculation summaries with clear guided step explanations today.
The highlighted point represents the current real-domain calculation.
The arcsine function reverses sine on a restricted interval. It returns one principal angle for each valid input. Real inputs must stay between negative one and one. This restriction comes from the sine function's output range. The principal arcsine range runs from negative ninety degrees. It ends at positive ninety degrees. In radians, that range is negative pi over two. It ends at positive pi over two.
Exact values are useful for common special angles. For example, arcsine of one half equals thirty degrees. The same answer equals pi over six radians. Radical inputs also appear often in trigonometry. Arcsine of square root two over two is forty-five degrees. Arcsine of square root three over two is sixty degrees. Negative inputs produce negative principal angles.
This calculator accepts decimals, fractions, and selected radical expressions. It also shows an exact result when recognized. Decimal output can use several precision levels. Degrees, radians, and gradians are supported. The verification line checks the answer using sine. Related cosine and tangent values are also displayed. A graph shows the increasing inverse sine curve. The active point is highlighted for valid real inputs.
Reverse mode starts with an angle instead. It calculates the corresponding sine value. Solve mode finds x from an arcsine equation. These modes help compare inverse and forward operations. Complex mode handles real inputs outside the usual domain. Those results include real and imaginary components. The complex logarithmic identity supports that extension.
Use exact forms for symbolic mathematics when possible. Use decimal forms for measurements and numerical work. Always check the selected angle unit carefully. Degree and radian values can look very different. The principal result is unique by definition. Other sine equations may have additional periodic solutions. Export tools save useful calculation details for later review. This calculator keeps inverse sine work clear and organized.
| x | Exact radians | Degrees | Decimal radians |
|---|---|---|---|
| -1 | -π/2 | -90° | -1.570796 |
| -√3/2 | -π/3 | -60° | -1.047198 |
| -√2/2 | -π/4 | -45° | -0.785398 |
| -1/2 | -π/6 | -30° | -0.523599 |
| 0 | 0 | 0° | 0 |
| 1/2 | π/6 | 30° | 0.523599 |
| √2/2 | π/4 | 45° | 0.785398 |
| √3/2 | π/3 | 60° | 1.047198 |
| 1 | π/2 | 90° | 1.570796 |
Arcsine is the inverse of sine on its principal interval.
The real domain is every x from negative one through one.
The range is -π/2 through π/2, inclusive.
Yes. Inputs such as 1/2 and -3/4 are supported.
Yes. Supported forms include sqrt(2)/2 and sqrt(3)/2.
Sine never produces two for any real angle.
Yes. Enable complex mode for real inputs outside the domain.
It shows a recognized symbolic angle using π when possible.
Yes. Both options export the current calculation summary.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.