1. What is Sin Inverse (Arcsin)?

The sin inverse function (arcsin) is the inverse of the sine function. It returns the angle whose sine is the given number. The output range is between -π/2 to π/2 radians or -90° to 90°.

2. How Does the Calculator Work?

The calculator computes the inverse sine (arcsine) of the input value using PHP's built-in asin() function, which returns the result in radians. You can choose to display the result in degrees or radians.

3. Mathematical Definition

Domain: -1 ≤ x ≤ 1
Range: -π/2 ≤ arcsin(x) ≤ π/2 (or -90° to 90°)
Relation to sine: sin(arcsin(x)) = x for all x in [-1, 1]
Principal value: The calculator returns the principal value (between -π/2 and π/2)

4. Using the Calculator

Tips:

• Enter a value between -1 and 1
• Choose whether you want the result in degrees or radians
• The result will be between -90° and 90° (or -π/2 and π/2 radians)

5. Frequently Asked Questions (FAQ)

Q1: Why is the input limited to -1 to 1?
A: The sine function only outputs values between -1 and 1, so its inverse is only defined for inputs in this range.

Q2: What's the difference between degrees and radians?
A: Degrees and radians are different units for measuring angles. 360° = 2π radians. Degrees are more common in everyday use, while radians are standard in higher mathematics.

Q3: Can I calculate arcsin for values outside [-1, 1]?
A: No, arcsin is undefined for values outside this range as no real angle has a sine value outside [-1, 1].

Q4: How precise is the calculation?
A: The calculator uses PHP's built-in functions which provide high precision (about 14 decimal places).

Q5: What about other inverse trig functions?
A: Similar calculators exist for arccos and arctan, each with their own domains and ranges.