1. What is Arc Sine Function?

The arc sine function (asin) is the inverse of the sine function. It returns the angle in radians whose sine is the given number. The output range is from -π/2 to π/2 radians.

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

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

Explanation: The arc sine function calculates the angle whose sine equals the input value x, with the result expressed in radians.

3. Mathematical Definition

Details: The arc sine function is defined for all x in the interval [-1, 1]. For any x in this range, there exists a unique angle θ in [-π/2, π/2] such that sin(θ) = x.

4. Using the Calculator

Tips: Enter a value between -1 and 1. The calculator will return the corresponding angle in radians. Invalid inputs outside this range will generate an error message.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arc sine output?
A: The arc sine function returns values in the range [-π/2, π/2] radians.

Q2: Can I use degrees instead of radians?
A: This calculator specifically works with radians. To convert to degrees, multiply the result by 180/π.

Q3: Why is the input restricted 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.

Q4: What about other inverse trigonometric functions?
A: This calculator specifically computes arc sine. Other calculators are available for arc cosine and arc tangent functions.

Q5: How precise are the results?
A: Results are calculated with high precision and rounded to 6 decimal places for readability.