1. What is Inverse Sine Function?

The inverse sine function (sin⁻¹ or arcsin) is the inverse of the sine function. It takes a ratio (between -1 and 1) and returns an angle whose sine is that ratio.

2. How Does the Calculator Work?

The calculator uses the inverse sine function:

Where:

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

Explanation: The function returns the principal value (between -π/2 and π/2 radians or -90° and 90°).

3. Mathematical Explanation

Details: The inverse sine function is defined for inputs between -1 and 1. For values outside this range, the result is undefined (not a real number).

4. Using the Calculator

Tips: Enter a value between -1 and 1. The calculator will return the angle in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of inverse sine?
A: The principal value range is [-π/2, π/2] radians or [-90°, 90°].

Q2: Why is the input limited to -1 to 1?
A: Because the sine of any real angle always produces a value between -1 and 1.

Q3: How is this different from cosecant?
A: Cosecant is the reciprocal of sine (1/sin), while inverse sine is the function that reverses the sine operation.

Q4: What about multiple solutions?
A: The calculator returns the principal value. The general solution would be θ + 2πn or π - θ + 2πn for any integer n.

Q5: When is inverse sine used?
A: Common applications include trigonometry, physics (wave equations), engineering, and computer graphics.