1. What is the Euler Angle Calculation Using Sin?

The Euler angle calculation using the sine function determines the angle θ from its sine value. This is based on the inverse sine (arcsine) function, which returns the angle whose sine is the given number.

2. How Does the Calculator Work?

The calculator uses the equation:

Where:

• \( \sin \theta \) — Sine of the angle (dimensionless, between -1 and 1)
• \( \theta \) — Euler angle in radians (converted to degrees for display)

Explanation: The arcsine function returns the principal value of the angle in the range [-π/2, π/2] radians, which is then converted to degrees.

3. Importance of Euler Angle Calculation

Details: Euler angles are fundamental in describing the orientation of a rigid body in three-dimensional space. They are widely used in computer graphics, robotics, aerospace, and physics to represent rotations.

4. Using the Calculator

Tips: Enter the sine value (must be between -1 and 1). The calculator will compute the corresponding angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why is the input range limited to [-1, 1]?
A: The sine function only outputs values between -1 and 1, so the input to the arcsine function must be within this range to yield a real number result.

Q2: What is the output range of the arcsine function?
A: The principal value range of arcsine is [-π/2, π/2] radians, or [-90°, 90°] in degrees.

Q3: Can this calculator handle angles beyond 90 degrees?
A: The arcsine function only returns angles in the range [-90°, 90°]. For angles outside this range, additional trigonometric considerations are needed.

Q4: How accurate is the calculation?
A: The calculation uses PHP's built-in asin() function, which provides high precision. The result is rounded to 4 decimal places for display.

Q5: What are common applications of Euler angles?
A: Euler angles are used in 3D modeling, flight dynamics, animation, and any field requiring representation of 3D rotations.