1. What is Inverse Sine (Arcsine)?

The inverse sine function (arcsine) calculates the angle whose sine is a given number. It's the reverse operation of the sine function, returning an angle from a sine value.

2. How Does the Calculator Work?

The calculator uses the arcsine formula:

Where:

• \( x \) — Input value between -1 and 1 (unitless)
• \( \arcsin(x) \) — Inverse sine in radians
• \( \frac{180}{\pi} \) — Conversion factor from radians to degrees
• \( \theta_{deg} \) — Resulting angle in degrees

Explanation: The calculator first computes the arcsine in radians, then converts the result to degrees by multiplying by 180/π (approximately 57.2958).

3. Understanding the Conversion

Details: While trigonometric functions in mathematics typically use radians, degrees are often more intuitive for practical applications. This calculator bridges that gap by providing results in degrees.

4. Using the Calculator

Tips: Enter any value between -1 and 1 (inclusive). The result will be an angle between -90° and 90° (the range of arcsine function).

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 (arcsine) is only defined for inputs in this range.

Q2: What's the difference between arcsin and sin^-1?
A: They mean exactly the same thing - both notations represent the inverse sine function.

Q3: Can I get results in radians instead?
A: Simply remove the (180/π) conversion factor - the result will then be in radians.

Q4: What about other inverse trig functions?
A: Similar calculators can be made for arccosine and arctangent using the same conversion principle.

Q5: Why might I need this calculation?
A: Useful in trigonometry, physics, engineering, and anywhere you need to find an angle from a known sine ratio.