1. What is Arcsin Function?

The arcsin function (inverse sine function) returns the angle whose sine is a given number. It is the inverse operation of the sine function, with output typically in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the arcsin mathematical function:

Where:

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

Explanation: The function calculates the principal value of the angle whose sine equals the input value.

3. Importance of Arcsin Calculation

Details: Arcsin is essential in trigonometry, physics, engineering, and computer graphics for solving problems involving angles when the sine value is known.

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 angle whose sine equals your input.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between radians and degrees?
A: Radians (0 to π) are the natural unit for angles in mathematics, while degrees (0° to 180°) are more common in everyday use. 180° equals π radians.

Q3: What is the range of arcsin output?
A: The principal value range is -π/2 to π/2 radians (-90° to 90°).

Q4: Can I calculate arcsin for complex numbers?
A: This calculator only handles real numbers. Complex arcsin requires more advanced mathematics.

Q5: How accurate is this calculation?
A: The calculation uses PHP's built-in asin() function which provides high precision (typically about 14 decimal places).