Question

What is the real meaning of "degree mode" and "radian mode"?

Answer 1

Apparently, degrees and radians both are measurement units for angles. However, they differ in one fundamental way. Degrees are not actual numbers, as they don't express absolute values, but just proportions.

In order to understand this, think about how we get the degrees. Take an angle with a fixed and a variable side. You can rotate the variable side until it completes a full circle. By convention, we decide that the full circle represents `360^0`. One degree is just that angle divided in 360 equal shares. The best analogy I can think of would be that between degrees and percentages. Both are just expressing proportions relative to a whole.

In turn, radians are actual numbers with which we can perform actual measurements and mathematical computations. .

For a detailed explanation, see this article .