Free · Trigonometry
Inverse Sine — Principal Angle
Find the principal inverse sine angle from a value between −1 and 1, with degree and radian units.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The inverse sine of 0.5 is 30°. The principal angle range is −90° to 90°, inclusive.
Angle = arcsine(x); reverse value = sine(angle)
Worked example
Enter these known values and leave the other values blank.
- Sine value x
- .5
- Principal inverse sine angle
- 30 deg
Assumptions and limitations
- The input value must lie between −1 and 1. The principal angle range is −90° to 90°, including endpoints.
- The inverse returns one principal angle, not every periodic angle with the same trigonometric value.
- Use the angle selector to distinguish degrees from radians. The inverse notation does not mean the reciprocal of sine.
Common questions
Does the inverse give every possible angle?
No. It gives the angle in the stated principal range. Other periodic solutions require separate consideration.
Can I enter the angle to recover the value?
Yes, provided the angle is within the principal range and its selected unit is correct.
References
Restrict reverse-entered angles to the principal inverse-sine interval, from minus ninety to ninety degrees.