RELATION BETWEEN RADIAN AND DEGREE

If a circle subtends at the center an angle whose radian measure is 2π and its degree measure is 360°. That is 

2π  =  360° and π  =  180°

The above relation enables us to express an radian measures in terms of degree measure and a degree measure in terms of radian measure.Using the approximate value of π as 22/7, we have 

1 radian  =  180°/π

1 radian  =  180°/π

1 radian  =  180°/3.14

1 radian  =  57° 19' approximately

Also, 1°  =  π/180° radian =  0.01745 radians approximately

The relation between degree measures and radian measure of some common angles are given in the following list.

  π/2  =  90°

  π/3  =  60°

  π/6  =  30°

  π/4  =  45°

  π  =  180°

  3π/2  =  270°

  2π  =  360°

Example 1 :

Convert 6 radians to degree measure.

Solution :

To convert 6 radians to degree, we need to use the formula.

Degree measure  =  (180°/π) x Radian measure 

6 radian  =  6 x (180°/π) radians

=  (180° x 6) / π

=  1080°/π

Substitute 3.14 for π and simplify.

≈  343.95°

Example 2 :

Convert 40° 30' to radian measure.

Solution :

To convert 40° 30' to radians, we need to use the formula.

Radian measure  =  (π/180°) x degree measure

40° 30' :

=  40° + 30'

=  40° + (30/60)°

=  40° + 0.5°

=  40.5°

=  40.5°

   =  40.5° x π/180° radians

Substitute 3.14 for π and simplify.  

≈  0.7065 radians

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