1. What is the Inverse Sine Function?

The inverse sine function (arcsin) is the inverse operation of the sine function. It takes a sine value between -1 and 1 and returns the corresponding angle whose sine is that value.

2. How Does the Calculator Work?

The calculator uses the inverse sine function:

Where:

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

Explanation: The function calculates the principal value (between -π/2 and π/2 radians or -90° and 90° for degrees) of the angle whose sine is the input value.

3. Understanding the Results

Details: The result represents the angle whose sine equals your input. Remember that multiple angles can have the same sine value due to periodicity.

4. Using the Calculator

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

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 inputs in this range.

Q2: What is the range of output values?
A: The principal values range from -π/2 to π/2 radians (-90° to 90°). This is the standard range for arcsin.

Q3: How accurate are the results?
A: Results are accurate to at least 4 decimal places, using PHP's built-in trigonometric functions.

Q4: Can I get angles outside the principal range?
A: The calculator only returns the principal value. For other solutions, you would need to consider the periodic nature of the sine function.

Q5: What's the difference between radians and degrees?
A: Radians (0 to 2π for full circle) are mathematically natural, while degrees (0° to 360°) may be more intuitive for some applications.