Page 127 - Mathematics_Form_3

Circles

Example 5.4 3. Find the angles in radians as
Convert each of the following radians multiples of π for each of the
into degrees: following degrees:
(a) 1.7 radians (a) 80° (b) 600°
FOR ONLINE READING ONLY
19π (c) 240° (d) 315°
____
(b) radians
4
4. Find the length of an arc of a circle
Solution
(a) Given s = 1. 7 radians. of radius10 cm, if the central angle
is:
πθ
, it follows that
From s = ____
180° (a) 1 radian (b) 0.14 radians
180° × 1. 7 (c) 2.5 radians
_________
θ = π

5. Convert each of the following
= 97 . 5°
radian angles in into degrees:
Therefore, 1.7 radians is equivalent
2 __
π __
to 97 . 5°. ( a ) (b) π
4 3
19π
____
(b) Given s = radians, then (c) π (d) π
3 __
7 __
4 4 2
180° s

θ = _____ . 6. Calculate the size of angles in
π
180° × 19π radians through which the minute
_________
⇒ θ =
π × 4 hand of a clock face turns between
= 855° 12.00 noon and the following times:
19π
____

Therefore, radians is equivalent (a) 12:40 pm (b) 3:00 pm
to 855° . 4
(c) 9:00 am
7. Find the size of the angles in radians
Mathematics for Secondary Schools 1. Convert each of the following 8. An automobile tyre has an outside
Exercise 5.3
through which the minute hand of
a clock turns between 12.00 noon
and the following times. Leave your
degrees into radians, leave your
answer in terms of π.
answer in π:
(a) 12:20 pm (b) 2:15 pm
(a) 10°
(b) 45°
(c) midnight
(c) 160°
2. Convert the following radians into
degrees. Give your answers correct
to two decimal places.
what angle, in radians, does the
wheel turn when the car travels a
(a) 1 radian (b) 0.3 radians diameter of 6 decimetres. Through
distance of one kilometre?
(c) 5 radians

120 Student\s Book Form Three

18/09/2025 09:59:36
MATHEMATIC F3 SB.indd 120
MATHEMATIC F3 SB.indd 120 18/09/2025 09:59:36