In trigonometry, the grade system (also known as gradians, gons, or grads) is an alternative way to measure angles, where a right angle is divided into 100 units.
Understanding Gradians
The grade system, employing gradians (or gons, grads, or grades), offers a different perspective on angle measurement compared to degrees. The key defining characteristic is:
- 1 gradian = 1/100 of a right angle.
Conversion Between Gradians and Degrees
Here's a simple relationship to convert between gradians and degrees:
- 100 gradians = 90 degrees
This relationship allows for easy conversions. For example:
- To convert from degrees to gradians, multiply the angle in degrees by (100/90).
- To convert from gradians to degrees, multiply the angle in gradians by (90/100).
Example Conversions
Here are a few examples to illustrate the conversion:
- Example 1: Convert 45 degrees to gradians.
- 45 degrees * (100/90) = 50 gradians
- Example 2: Convert 200 gradians to degrees.
- 200 gradians * (90/100) = 180 degrees
Why Use Gradians?
While degrees are the more common unit in many areas of mathematics and physics, gradians were initially introduced with the metric system to potentially simplify some calculations. However, degrees remain the dominant unit in most practical applications.
