This document contains information about angles and their measurement in radians. It includes examples of converting between radians and degrees, finding arc lengths and sector areas of circles using radians, and solving related problems. Formulas used include defining 1 radian as the angle subtended by an arc equal in length to the circle's radius, and the sector area formula A = 1/2 * r^2 * θ (in radians).

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Section 6.1
Angles and Their Measure

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Radians

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Find the length of the arc of a circle of radius 4 meters
subtended by a central angle of 0.5 radian.
( ) ( )4 0.5 2 meterss = =

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(a) 30° (b) 120° (c) – 60° (d) 270° (e) 104 °
0 radian
30 radians
180
(a)
6
π π 
= ÷
° 
0 radian 2
0 radians
180 3
(b) 12
π π 
= ÷
° 
0 radian
0 radians
180 3
(c) 6
π π
−
 
= − ÷
° 
0 radian 3
0 radians
180 2
(d) 27
π π 
= ÷
° 
0 radian
1.815 radians
180
(e) 104
π 
≈ ÷
° 

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5
(a) radian (b) radian (c) radians (d) 5 radians
3 2 6
π π π
−
180
(a) 60
3
π
π
° 
= ° ÷
 
180
(b) 90
2
π
π
° 
− = − ° ÷
 
5 180
(c) 150
6
π
π
° 
= ° ÷
 
180
(d) 5 286.48
π
° 
= ° ÷
 

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Find the area of the sector of a circle of radius 5 feet formed
by an angle of 60°. Round the answer to two decimal places.
In order to use the equation for the area of a sector, must be in radians.
60
180 3
θ
π π
θ
 
= ° = ÷
° 
( )
21 25
5 13.09 square feet
2 3 6
A
π π 
= = ≈ ÷
 