How many radians are there in 360 degrees?

In the context of converting degrees to radians, it's important to understand the relationship between these two units of measurement. Radians are based on the radius of a circle, while degrees are a more traditional measurement system.

A full circle is defined as 360 degrees. To convert degrees to radians, we use the fact that 180 degrees is equal to π radians. This means that for the full circle of 360 degrees, if we set up a proportion based on this relationship, we can determine how many radians are in 360 degrees.

Using the conversion formula:

• Start with the equivalence: 180 degrees = π radians.

• Since 360 degrees is double 180 degrees, we double π.

Thus, 360 degrees is equal to 2π radians. This provides a clear understanding of why the correct answer is that there are 2π radians in a full circle or 360 degrees.