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Circles

Therefore, from noon to 1:15 pm, the
12
11 1 minute hand turns through 450° or π
5 __
10 2 radians. 2

9 3 Example 5.3
FOR ONLINE READING ONLY
8 4 Convert each of the following degrees

7 5 into radians as a multiple of :
6
(a) 165°
Figure 5.5: A clock face showing an
angle of 90° or radians. (b) 225°
π __
2
From noon to 12:45 pm, the minute Solution
hand turns through an angle of 270°
(a) Recall the formula for computing
3π
or radians. The angle 270° is a reflex the radian measure:
___
2
angle as shown in Figure 5.6. πθ
.
s = ____
180°
12
11 1 Given θ = 165° , substituting into
10 2 the formula gives
165° × π
9 3 s = _______

180°
8 4 11π
= ____ radians
7 5 12
6
Therefore, 165° is equivalent
Figure 5.6: Turn of the minute hand at 11π
____
3π to 12 radians.
___
270° or radians
2 πθ
and θ = 225° , it
One complete turn of the hand of a clock (b) From s = ____
180°
represents an angle of 360° or 2π radians. implies that
Measures of angles of more than 360° s = _______
225° × π

or 2π radians can be obtained if the 180° Mathematics for Secondary Schools
minute hand of a clock makes more than = radians
5π
___
one complete turn. For instance, from 4
5π
___
noon to 1:15 pm, the minute hand turns Therefore, 225° is equivalent to
4
5 __
through turns. Since one turn is 360°or radians.
4
5 __
5 __
2π radians, then turns is 360° × or
4 4
2π × radians, which gives 450° or π
5 __
5 __
4 2
radians.
Student\s Book Form Three 119

MATHEMATIC F3 SB.indd 119 18/09/2025 09:59:36
18/09/2025 09:59:36
MATHEMATIC F3 SB.indd 119