Page 85 - Math SL HB Sem 1

( ]I I{C U LA IT I,'T] NC'TI ONS AND,f ItI(; ON O]VIE'I.RY

THE CIRCLE: Radian measure of angles

An angle of'one radian is the angle sutrtended by an arc oflength
one unit at lhe center of the unit circle.

Y
r0, l.i
(0, l)

I unr(
X ? unirJ
, 0)
(1. 01 x

figure I
I)gure 2
*one
radian is also the size of the angle subtended at the centre ot_a circle ol
radius r by an arc of length r.

The angle subtended by the whore circumference
ofunit circle at the centre is 360"
and since the length of the circumfe rence is 2 r unlr., *" hur"

2zr radians :360"
I radian - 57.3" ( 3 significant tigures)

The advantage ofusing radian measure ofan angle is that it measures the angle in
terms of arc length.

Degree-radian conversions

,T
r80

Degrecs
Iladians

180
,1
,T

4-l