Page 85 - Math SL HB Sem 1

(]IRCLI
LAR FUNC'IIONS AND TRI(;ONO]VIEI'RY

THE CIRCLE: Radian measure of angles

An anglc of'one radian is the angle subtenrlcd by an arc oflength
onc unit al the ccnter of the unit circle.

\,
Y
(0. l)
(0. l)

I trnrt
x I unitJ
(l,0)

{r, 0) X

figure I
frgure 2
*one
radian is also the size of the angle subtended at the centre ol.a circle of
radius r by an arc oflength r.

The a.ngle subtended by the whore circumference
of unit circre at the centre is 360o
and since the length of the circumle rence is 2 zru nitr, ,r. truu"

2;r radians = 360"
I radian = 57.3" ( 3 significant figures)

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

Degree-radian conversions

1f
180

Degrees
Radians

180
\ ,1
7T

4-l