1. What is Degree Mode?

Degree mode refers to the unit of measurement for angles where a full circle is divided into 360 degrees. This is the most common unit for measuring angles in everyday applications.

2. How Does the Calculator Work?

The calculator uses these conversion formulas:

Where:

• \( \pi \) — Mathematical constant (≈3.14159)
• 1 radian ≈ 57.2958 degrees
• 1 degree ≈ 0.0174533 radians

Explanation: These formulas allow conversion between the two most common angle measurement systems used in mathematics and science.

3. Importance of Angle Conversion

Details: Converting between degrees and radians is essential in trigonometry, physics, engineering, and computer graphics where different systems may be required.

4. Using the Calculator

Tips: Enter the angle value, select the conversion direction (degrees to radians or vice versa), and click calculate. The result will show the converted value with appropriate units.

5. Frequently Asked Questions (FAQ)

Q1: When should I use degrees vs radians?
A: Degrees are common in everyday applications, while radians are preferred in higher mathematics and physics calculations.

Q2: Why are there 360 degrees in a circle?
A: This dates back to ancient Babylonian astronomy which used a base-60 number system and divided the circle into 360 parts.

Q3: What's the advantage of using radians?
A: Radians provide a more natural measurement in calculus and physics where angles are related to arc lengths and circular motion.

Q4: How precise are these conversions?
A: The calculator uses double-precision floating point arithmetic with π accurate to about 15 decimal places.

Q5: Can I convert negative angles?
A: Yes, negative angles represent rotation in the opposite (clockwise) direction and convert the same way as positive angles.