1. What is Radians to Degrees Conversion?

The conversion between radians and degrees is a fundamental operation in trigonometry and mathematics. While degrees divide a circle into 360 parts, radians provide a measurement based on the radius of the circle.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( \theta_{rad} \) — Angle in radians
• \( \pi \) — Mathematical constant Pi (~3.14159)
• \( \theta_{deg} \) — Resulting angle in degrees

Explanation: Since 180° equals π radians, multiplying radians by 180/π converts them to degrees.

3. Importance of Angle Conversion

Details: Many mathematical functions use radians, while many practical applications use degrees. Conversion between these units is essential in fields like physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the angle value in radians. The calculator will automatically compute the equivalent value in degrees. Negative values are acceptable and represent angles measured in the opposite direction.

5. Frequently Asked Questions (FAQ)

Q1: Why do we need both radians and degrees?
A: Radians are mathematically "natural" for calculus and trigonometric functions, while degrees are more intuitive for human understanding and many practical applications.

Q2: What's the conversion factor from degrees to radians?
A: To convert degrees to radians, multiply by π/180 (approximately 0.0174533).

Q3: What are some common angle equivalents?
A: 360° = 2π rad, 180° = π rad, 90° = π/2 rad, 45° = π/4 rad, etc.

Q4: When should I use radians vs degrees?
A: Use radians for mathematical calculations (especially calculus), degrees for practical measurements and visualizations.

Q5: Does this conversion work for all angle values?
A: Yes, the conversion works for any real number input, including values greater than 2π or negative values.