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# RELATION BETWEEN DEGREES AND RADIANS

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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.

 The formula for converting radians to degrees:

Example

Convert 2.4 radians measure into degree measure

Use the formula for converting radians to degrees:

Substitute the radian as follows:

 The formula for converting degrees to radians:

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:

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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