Arcsin in Degrees Calculator
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Reviewed by Calculator Editorial Team
The arcsin in degrees calculator computes the inverse sine function, which returns the angle whose sine is the given value. This is useful in trigonometry, physics, and engineering applications where you need to find angles from known sine values.
What is Arcsin?
The arcsin function, also known as the inverse sine function, is the mathematical operation that returns the angle whose sine is a given value. It's defined for inputs between -1 and 1, with outputs ranging from -90° to 90°.
In practical terms, if you know the ratio of the opposite side to the hypotenuse in a right triangle (the sine value), arcsin will tell you the angle opposite that side.
Note: The arcsin function is not defined for values outside the range [-1, 1]. Attempting to calculate arcsin of a number outside this range will result in an error.
How to Use the Calculator
- Enter a value between -1 and 1 in the input field.
- Select whether you want the result in degrees or radians.
- Click "Calculate" to see the result.
- The calculator will display the angle in the selected units.
For example, if you enter 0.5, the calculator will return 30° if you select degrees, or approximately 0.5236 radians if you select radians.
Formula
The formula for arcsin in degrees is:
θ = arcsin(x) × (180° / π)
Where:
- θ is the angle in degrees
- x is the input value (must be between -1 and 1)
- π is the mathematical constant pi (approximately 3.14159)
The calculator uses this formula to convert the result from radians (the native output of the arcsin function) to degrees when requested.
Examples
| Input Value | Result in Degrees | Result in Radians |
|---|---|---|
| 0 | 0° | 0 rad |
| 0.5 | 30° | 0.5236 rad |
| 1 | 90° | 1.5708 rad |
| -0.5 | -30° | -0.5236 rad |
| -1 | -90° | -1.5708 rad |
These examples demonstrate how the arcsin function works for different input values. The calculator can handle both positive and negative values within the defined range.
FAQ
What is the range of the arcsin function?
The arcsin function is defined for inputs between -1 and 1. The output range is from -90° to 90° in degrees or from -π/2 to π/2 in radians.
Can I use this calculator for complex numbers?
No, this calculator only works with real numbers between -1 and 1. Complex numbers are not supported.
Why does the calculator show an error for values outside -1 to 1?
The arcsin function is mathematically undefined for values outside the range [-1, 1]. The calculator includes validation to prevent such inputs.
How accurate are the results?
The calculator uses JavaScript's built-in Math.asin() function, which provides accurate results within the limits of floating-point arithmetic.