1. What is the Inverse Sine Function?

The inverse sine function (arcsin) is the inverse of the sine function. It takes a value between -1 and 1 and returns an angle whose sine is that value. The output range is [-π/2, π/2] in radians or [-90°, 90°] in degrees.

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

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

Explanation: The function returns the principal value (the angle between -π/2 and π/2 radians or -90° and 90°) whose sine is x.

3. Mathematical Properties

Details: The arcsin function is defined only for inputs between -1 and 1. It's an odd function (arcsin(-x) = -arcsin(x)) and is the inverse of the sine function on its principal domain.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select whether you want the result in radians or degrees. The calculator will return the principal value of the inverse sine.

5. Frequently Asked Questions (FAQ)

Q1: Why is the input restricted to -1 to 1?
A: The sine function only outputs 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 (range -π/2 to π/2) are the natural mathematical unit, while degrees (range -90° to 90°) may be more intuitive for some applications.

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

Q4: How is this related to trigonometry?
A: The arcsin function is essential for solving triangles when you know the ratio of sides but need to find the angle.

Q5: What about complex numbers?
A: This calculator only handles real numbers. For complex numbers, arcsin is defined but requires more advanced mathematics.