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.