Arc Length and Radians

r

2r =D

r =radiusD =diameterC =circumfrance

C

D=π =3.14159

C2r

=π

C =2πrC2π

=r

C2π

=Sθ=r

S =rθθ is measured in radians

θ =2π

S = r2π = C

2π rad = 360o

1rad =360o

2π= 57.3deg

rad

Small Angle ApproximationSmall-angle approximation is a useful simplification of the laws of trigonometry

which is only approximately true for finite angles.

FOR θ ≤10o

10o =0.174532925 radians

sinθ ; θ

sin(10o ) =0.173648178

EXAMPLE