1. What is Inverse Sine?

The inverse sine function (arcsin) is the inverse operation 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
• \( \theta \) — Output angle in radians or degrees

Explanation: The function calculates the principal value of the angle (between -π/2 and π/2 radians or -90° and 90°) whose sine equals the input value.

3. Importance of Inverse Sine Calculation

Details: Inverse sine is crucial in trigonometry, physics, engineering, and computer graphics for determining angles from known ratios. It's used in solving triangles, analyzing waveforms, and many other applications.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select your preferred output unit (radians or degrees). The calculator will return the angle whose sine equals your input value.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between radians and degrees?
A: Radians and degrees are different units for measuring angles. 360° = 2π radians. Radians are often preferred in mathematical calculations.

Q3: Why does arcsin sometimes return NaN?
A: If you input a value outside [-1, 1], the result is "Not a Number" (NaN) since no real angle has a sine outside this range.

Q4: Is arcsin the same as sin⁻¹?
A: Yes, arcsin and sin⁻¹ are two notations for the same inverse sine function.

Q5: What about other solutions outside the principal range?
A: The calculator returns the principal value. Other solutions can be found using trigonometric identities and periodicity.