Radian Measure

 

 

 

Contents

 

Radian & Degree

 

Arc Length

 

Area of Sector

  

Quiz

 

 

Geometry Main Page 

Radian & Degree

 

Introducing the Radian 

The angle subtended at the centre of a circle by an arc equal in length is 1 radian.

In general, if the length of the arc is s units and the radius is r units, the . The size of the angle is the ratio of the arc length to the length of the radius.

Example

If s= 3cm and r = 2cm, calculate q.

  
      = 3/2
      = 1.5 rad.
 
Relation between Radian and Degree Measures
 
In general, p radian = 180°
 
Proof:
 
s = ½(2 pr) = pr
   = (pr)/r
   = p radian
 
Since q = 180°, so p radian = 180°

 
Example 1
 
Convert p/8 rad. to degrees.
 
180º/8 = 25°

Example 2
 
Convert 330° to radians.
 
330°/180° x p = 11p/6 rad.