Arcsin Calculator in Degrees

The arcsin calculator in degrees helps you find the angle whose sine is a given value. This is useful in trigonometry, physics, and engineering when you need to determine an angle from a known sine value.

What is arcsin?

The arcsine function, also known as the inverse sine function, is the inverse of the sine function. While the sine function takes an angle and returns a ratio, the arcsine function takes a ratio and returns an angle.

In mathematical terms, if sin(θ) = y, then arcsin(y) = θ. The result is always in the range of -90° to 90° because the sine function is periodic and symmetric.

The arcsin function is only defined for inputs between -1 and 1, inclusive. If you provide a value outside this range, the calculator will return an error.

How to use this calculator

Enter a value between -1 and 1 in the input field.
Click the "Calculate" button to compute the arcsine in degrees.
View the result in the result panel below the calculator.
Use the "Reset" button to clear the input and result.

The calculator will display the result in degrees with two decimal places of precision. If you need more precision, you can modify the JavaScript code.

Formula and calculation

The arcsin function in degrees is calculated using the following formula:

arcsin(y) = sin⁻¹(y) × (180° / π)

Where:

y is the input value (must be between -1 and 1)
sin⁻¹(y) is the inverse sine function in radians
180° / π is the conversion factor from radians to degrees

The calculator uses the JavaScript Math.asin() function, which returns the arcsine in radians, and then converts the result to degrees by multiplying by 180/π.

Practical examples

Example 1: Basic calculation

If sin(θ) = 0.5, then θ = arcsin(0.5) = 30°.

This is because sin(30°) = 0.5, and the arcsine function returns the angle whose sine is 0.5.

Example 2: Negative input

If sin(θ) = -0.5, then θ = arcsin(-0.5) = -30°.

The negative input results in a negative angle, which corresponds to the angle in the fourth quadrant.

Example 3: Edge case

If sin(θ) = 1, then θ = arcsin(1) = 90°.

This is the maximum value of the sine function, which occurs at 90°.

FAQ

What is the range of the arcsin function?: The arcsin function returns values in the range of -90° to 90° because the sine function is periodic and symmetric.
What happens if I enter a value outside the range of -1 to 1?: The calculator will display an error message because the arcsin function is only defined for inputs between -1 and 1.
How is the result displayed?: The result is displayed in degrees with two decimal places of precision. You can modify the JavaScript code to display more or fewer decimal places.
Can I use this calculator for angles outside the range of -90° to 90°?: No, the arcsin function is only defined for angles in the range of -90° to 90°. If you need to find an angle outside this range, you may need to use additional trigonometric functions or context-specific information.
Is the arcsin function the same as the inverse sine function?: Yes, the arcsin function and the inverse sine function are the same. They both return the angle whose sine is a given value.