Sin-1 Calculator Degrees

The sin-1 calculator (also called arcsine calculator) finds the angle whose sine is a given value. This calculator works in degrees and provides both the principal value and all possible values within the range of the sine function.

What is sin-1?

The inverse sine function, written as sin-1 or arcsin, is the inverse of the sine function. While the sine function takes an angle and returns a ratio, the inverse sine function takes a ratio and returns an angle.

For any real number x between -1 and 1, there are infinitely many angles θ such that sin(θ) = x. However, the principal value of sin-1(x) is the angle θ in the range [-90°, 90°] that satisfies sin(θ) = x.

Key Properties

The domain of sin-1 is [-1, 1]
The range of sin-1 is [-90°, 90°]
sin-1(sin(θ)) = θ only when θ is in [-90°, 90°]
sin(sin-1(x)) = x for all x in [-1, 1]

How to use this calculator

Enter a value between -1 and 1 in the input field
Click "Calculate" to find the angle in degrees
View the principal value and all possible values
Use the chart to visualize the relationship

The calculator will display the principal value (the angle between -90° and 90°) and all possible values (angles between -180° and 180° that satisfy the equation).

Formula

Principal Value

sin-1(x) = θ where θ is in [-90°, 90°] and sin(θ) = x

All Possible Values

sin(θ) = x has solutions θ = sin-1(x) + 360°n and θ = 180° - sin-1(x) + 360°n for any integer n

The calculator uses JavaScript's built-in Math.asin() function which returns the principal value in radians, then converts it to degrees.

Examples

Input (x)	Principal Value (degrees)	All Possible Values (degrees)
0.5	30°	30°, 150°, -330°, -150°, etc.
-0.5	-30°	-30°, -150°, 330°, 150°, etc.
1	90°	90°, 270°, -90°, -270°, etc.

For example, if you enter 0.5, the calculator will show that the principal value is 30° and all possible values are 30°, 150°, -330°, -150°, etc.

FAQ

What is the difference between sin-1 and arcsin?: sin-1 and arcsin are the same function, written differently. Both represent the inverse sine function.
Why does the calculator show multiple values?: The sine function is periodic with a period of 360°, so there are infinitely many angles that satisfy sin(θ) = x. The calculator shows the principal value and the next few values within the range [-180°, 180°].
What happens if I enter a number outside [-1, 1]?: The calculator will display an error message because the sine function only outputs values between -1 and 1. The inverse sine function is only defined for inputs in this range.
How accurate is this calculator?: The calculator uses JavaScript's built-in Math.asin() function which provides accurate results to approximately 15 decimal places. The conversion to degrees is also precise.
Can I use this calculator for complex numbers?: No, this calculator only works with real numbers between -1 and 1. For complex numbers, you would need a different type of calculator.