Arcsin in Degrees Google Calculator
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Reviewed by Calculator Editorial Team
The arcsin function (also known as inverse sine) calculates the angle whose sine is a given value. This calculator helps you find arcsin in degrees using Google Calculator's capabilities.
What is arcsin in degrees?
The arcsin function is the inverse of the sine function. While sine takes an angle and returns a ratio, arcsin takes a ratio and returns an angle. When working with degrees, arcsin gives you the angle measure in degrees that corresponds to a specific sine value.
This is particularly useful in trigonometry, physics, and engineering where you need to find angles from known sine values. The range of arcsin in degrees is typically from -90° to 90°.
How to calculate arcsin in degrees
To calculate arcsin in degrees using Google Calculator:
- Enter your sine value in the calculator below
- Click "Calculate" to get the result in degrees
- Review the formula and assumptions used
- Understand the result and its implications
The calculator will handle the conversion from radians to degrees automatically, giving you a precise angle measurement.
Formula and assumptions
Formula
arcsin(x) in degrees = asin(x) × (180/π)
Where:
- x is the sine value (must be between -1 and 1)
- asin(x) is the inverse sine function in radians
- 180/π is the conversion factor from radians to degrees
Assumptions
- The input value must be between -1 and 1
- The result will be in degrees
- For values outside the domain, the calculator will show an error
Worked examples
Example 1: Basic arcsin calculation
If sin(θ) = 0.5, what is θ in degrees?
Using the formula:
θ = arcsin(0.5) = asin(0.5) × (180/π) ≈ 30°
This means the angle whose sine is 0.5 is 30 degrees.
Example 2: Negative sine value
If sin(θ) = -0.866, what is θ in degrees?
Using the formula:
θ = arcsin(-0.866) = asin(-0.866) × (180/π) ≈ -60°
This means the angle whose sine is -0.866 is -60 degrees.
Frequently asked questions
What is the range of arcsin in degrees?
The range of arcsin in degrees is from -90° to 90°. This is because the sine function is periodic and symmetric.
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.
How accurate is this calculator?
The calculator uses JavaScript's built-in Math.asin() function which provides accurate results to about 15 decimal places.