Relation between Degrees and Radians
A radian is a measure of an angle, indicating the ratio between the arc length and the radius of a circle, which is expressed as follows:
Since, the arc length of a full circle is the same as the circumference of a circle, which is written as, then, the radian of the full circle is:
The radian measure of angle:
The circular measure of angle means the number of radians a circle contains. Hence, the radian (circular) measure of a right angle is.

Example
Convert 2.4 radians measure into degree measure
Use the formula for converting radians to degrees:
Substitute the radian as follows:

Example
Convert into radian measure
Use the formula for converting degrees to radians:
Substitute the degree as follows:
The relationship between degree measure and radian measures for some standard angles are given below:
Degrees 
Radians 
Question 1:
Convert 1 radian into degree measure.
Solution
Question 2:
Convert 5. 2 radians measure into degree measure
Solution
Use the formula for converting radians to degrees:
Substitute the radian as follows:
Therefore, 5. 2 radian is converted to .
Question 3:
Convert into radian measure
Solution
Use the formula for converting degrees to radians:
Substitute the degree as follows:
Therefore, is converted to 3.49 radians.
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