1. What is the Arcsin Function?

The arcsin function (also called inverse sine) is the inverse of the sine function. It returns the angle whose sine is the given number. The output range is limited to [-π/2, π/2] radians or [-90°, 90°].

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

• \( x \) — Input value between -1 and 1
• \( \theta \) — Output angle in radians or degrees

Explanation: The calculator first computes the arcsine in radians, then converts to degrees if requested.

3. Mathematical Explanation

Details: The arcsine function is defined for real numbers only in the domain [-1, 1]. For values outside this range, the result would be complex.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select your preferred output unit (radians or degrees). The calculator will return the principal value of the arcsine.

5. Frequently Asked Questions (FAQ)

Q1: Why is the input limited to -1 to 1?
A: The sine function only produces values between -1 and 1, so its inverse is only defined for inputs in this range.

Q2: What's the difference between radians and degrees?
A: Radians (0 to 2π for full circle) are mathematically natural, while degrees (0 to 360) are more common in everyday use. 1 radian ≈ 57.2958°.

Q3: Are there multiple solutions to arcsin(x)?
A: Mathematically yes, but the calculator returns the principal value between -π/2 and π/2 radians (-90° to 90°).

Q4: How is arcsin related to other inverse trig functions?
A: arcsin(x) = arccos(√(1-x²)) = arctan(x/√(1-x²)) for x in (-1,1).

Q5: What about complex numbers?
A: For |x| > 1, arcsin(x) would be complex. This calculator only handles real-valued results.