S3 - G3 : Arc Length, Area of Circle using Degree and Radian

Degree and Radian (Unit of Measures) for angles 

Radian is defined as the angle from the centre of a circle which intercepts an arc equal in length to the radius of the circle.

Both degree and radian is a measure of angle.

                  360^o = 2π rad

                 => 1^o = 2π rad / 360^o

  

  2π rad = 360^o

         =>   1 rad = 360^o / 2π

Converting between Degree and Radian

                  360^o = 2π rad

Example

What is the value of 240^o in rad?

    360^o = 2π rad 

                240^o = 2π rad x 240^o

                                 360^o

                        = 4π/3 rad

Example

What is the value of 3 radian in degree?

           2π rad = 360^o

                           1 rad = 360^o / 2π

                           3 rad = 360^o x 3 / 2π

                                    = 171.81^o

	Degree	Radian
	1o =  π   rad        180	1 rad = 180o               π
Circle	360	2πrad
Circumference	2πr	2πr
Arc(S)	θ    x 2πr 360	rθ
Area of circle	πr2	πr2
Area(segment)	θ    x πr2 360	1   r2 θ      2

Circles
                                 
   Formula

                      Angle at centre is twice angle at circumference