1. What is Arc Sine?

The arc sine function (also called inverse sine) is the inverse of the sine function. It returns the angle whose sine is the given number. The result is typically expressed in degrees or radians.

2. How Does the Calculator Work?

The calculator uses the arc sine formula:

Where:

• \( x \) — Input value between -1 and 1
• \( \sin^{-1} \) — Inverse sine function
• \( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The calculator first computes the inverse sine in radians, then converts the result to degrees using the conversion factor.

3. Importance of Arc Sine Calculation

Details: Arc sine calculations are essential in trigonometry, geometry, physics, engineering, and computer graphics for determining angles from known sine values.

4. Using the Calculator

Tips: Enter a value between -1 and 1. The calculator will return the corresponding angle in degrees. Valid input range is -1 to 1 inclusive.

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 this range.

Q2: What's the difference between degrees and radians?
A: Degrees and radians are different units for measuring angles. 180 degrees equals π radians. This calculator provides results in degrees.

Q3: Can I calculate arc sine for values outside -1 to 1?
A: No, the arc sine function is undefined for values outside the range [-1, 1] as these values cannot be produced by the sine function.

Q4: What are typical applications of arc sine?
A: Arc sine is used in navigation, physics (especially wave mechanics), computer graphics, and anywhere angles need to be determined from trigonometric ratios.

Q5: How accurate is this calculator?
A: The calculator uses PHP's built-in asin() function which provides high precision results, rounded to 4 decimal places for display.