Circular Measure
Chapter 8- Circular Measure
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
CHAPTER 8- CIRCULAR MEASURE
8.1 RADIAN 1. In lower secondary, we have learned the unit for angle is degree. In this chapter, we will learn one more unit for angle that is radian. P r O 1 radian r Q 2. When the value of the angle 1 radian, then the length of the arc is equal to the length of the radius. 3. From this information, we can deduce that: r
1 rad r = 360 2πr
1 rad = r 2πr × 360
2π rad = 360°
4. π rad = 180°
1 rad =
180°
π
= 57.3° or 57°18 '
5. 2π rad = 360°
1° =
π
180
radian
8.1.1 Converting Measurements in degree to radian Example 1: Convert 120° to radians Solution:
1° =
π
180
radian
Page | 94
Chapter 8- Circular Measure
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
120° = 120 × =
π
180
radian
2π radian or 2.0947 radian 3
Tips
Example 2: Convert 112°36 ' to radians Solution:
1° = 60'
112°36 ' = 112° + 36 ' 36 = 112° + ( )° 60 = 112° + 0.6° = 112.6° π 1° = radian 180 π 112.6° = 112.6 × radian 180
= 1.965 rad 8.1.2 Converting Measurements in radian to degree Example 1: Convert
π
6
rad to degree
Solution:
1 rad =
180°
π π π 180° rad = × 6 6 π
= 30°
Example 2: Convert 1.36rad to degree Solution:
1 rad =
180°
π
Page | 95
Chapter 8- Circular Measure
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
1.36rad = 1.36 × = 244 °
180°
π
π
= 77.92°
EXERCISE 8.1 1. Convert each of the following values to degrees and the nearest minute. (π = 3.142 ) (a) 0.37 rad (b) 2.04 rad (c) 1.19 rad 2. Convert each of the following values to radians, giving your answer correct to 4 significant figures.
(π
= 3.142)
(a) 248°9 ' (b) 304°22 ' (c) 46°14 ' 8.2 LENGTH OF ARC OF A CIRCLE P S
θ
O Q
S Circumference of a circle
=
θ angle of a whole turn
If the unit of angle is degrees, The angle of a whole turn is
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
CHAPTER 8- CIRCULAR MEASURE
8.1 RADIAN 1. In lower secondary, we have learned the unit for angle is degree. In this chapter, we will learn one more unit for angle that is radian. P r O 1 radian r Q 2. When the value of the angle 1 radian, then the length of the arc is equal to the length of the radius. 3. From this information, we can deduce that: r
1 rad r = 360 2πr
1 rad = r 2πr × 360
2π rad = 360°
4. π rad = 180°
1 rad =
180°
π
= 57.3° or 57°18 '
5. 2π rad = 360°
1° =
π
180
radian
8.1.1 Converting Measurements in degree to radian Example 1: Convert 120° to radians Solution:
1° =
π
180
radian
Page | 94
Chapter 8- Circular Measure
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
120° = 120 × =
π
180
radian
2π radian or 2.0947 radian 3
Tips
Example 2: Convert 112°36 ' to radians Solution:
1° = 60'
112°36 ' = 112° + 36 ' 36 = 112° + ( )° 60 = 112° + 0.6° = 112.6° π 1° = radian 180 π 112.6° = 112.6 × radian 180
= 1.965 rad 8.1.2 Converting Measurements in radian to degree Example 1: Convert
π
6
rad to degree
Solution:
1 rad =
180°
π π π 180° rad = × 6 6 π
= 30°
Example 2: Convert 1.36rad to degree Solution:
1 rad =
180°
π
Page | 95
Chapter 8- Circular Measure
Additional Mathematics Module Form 4 SMK Agama Arau, Perlis
1.36rad = 1.36 × = 244 °
180°
π
π
= 77.92°
EXERCISE 8.1 1. Convert each of the following values to degrees and the nearest minute. (π = 3.142 ) (a) 0.37 rad (b) 2.04 rad (c) 1.19 rad 2. Convert each of the following values to radians, giving your answer correct to 4 significant figures.
(π
= 3.142)
(a) 248°9 ' (b) 304°22 ' (c) 46°14 ' 8.2 LENGTH OF ARC OF A CIRCLE P S
θ
O Q
S Circumference of a circle
=
θ angle of a whole turn
If the unit of angle is degrees, The angle of a whole turn is