Question

In science and engineering, radians are much more convenient (and common) than degrees. What is the degree value for one radian?

1) 180 degrees
2) 90 degrees
3) 45 degrees
4) 360 degrees

Answer 1

The degree value for one radian is approximately 57.3 degrees, as 2π radians are equal to 360 degrees.

Step-by-step explanation:

The degree value for one radian is approximately 57.3 degrees. This is derived from the relationship that 2π radians equal one full revolution, which is also equivalent to 360 degrees. Since 2π radians are equal to 360 degrees, dividing both sides of the equation by 2π gives us the conversion from radians to degrees, which is:

1 radian = 360 degrees / 2π = 57.2958 degrees (approximately).

Therefore, from the available choices, 1 radian is closest to option:

1. 57.3 degrees

The degree value for one radian is 57.3 degrees.

There is a conversion factor between radians and degrees, which is 1 radian = 57.3 degrees. This conversion factor allows us to convert between these two units of angle measurement.