8.1.
Degree measure is based on the division of a circle
on 360 parts which is artificial decision.
8.2.
It is a sector in a circle such that the arc is
equal to the radius.
8.3.
Radian measure allows to relate linear (length
of arc)and angular (value of central angle) measures
in a simplest form.
8.4.
The length of the arc AB equals the measure of
the angle
(in radians):
arcAB = .
Since AB = 2·sin /2,
we get AB = 2·sin (arcAB/2).
8.5.
The agent 0.017 provides connection between radian
and degree measures: he tells how many radians
there are in one degree.
8.6.
Any proportion which contains a known relation
between degrees and radians. For instance this
one:
180° 
°
 _{r}
8.7.
1) 518
0.87 ; 2) 140°
8.8.
Let 3x, 4x and 5x be measures of the angles. Then
3x + 4x + 5x = .
From here,
x = /12
and the angles are 4,
3,
and 512.
8.9.
Since the entire circle contains 2
radians; the number of cars is 2/(/8)
= 16.
Length = Radius·
= 8·(/8)
=
3.14 (m).
8.10.
By formula (8.1), s = ·r
= 6·30 = 180
(m/min)..
8.11.
From formula (8.1),
= s/r = 48/150 = 0.32 (radians).
The second hand makes the full rotation of 2
radians in 60 seconds. Therefore, it will make
the rotation of 0.32 radians in 0.32·60/(2)
3 seconds.
8.12
8.13.
