ABSTRACT
Problem 7. Express in radians, in terms of π: (a) 150◦ (b) 270◦ (c) 37.5◦
Since 180◦ =π rad then 1◦ = 180/π, hence
(a) 150◦ = 150 ( π
) rad = 5π
6 rad
(b) 270◦ = 270 ( π
) rad = 3π
2 rad
(c) 37.5◦ = 37.5 ( π
) rad = 75π
360 rad = 5π
24 rad
Now try the following exercise
Exercise 72 Further problems on radians and degrees
1. Convert to radians in terms of π: (a) 30◦ (b) 75◦ (c) 225◦ [
(a) π 6
(b) 5π 12
(c) 5π 4
]
2. Convert to radians: (a) 48◦ (b) 84◦ 51′ (c) 232◦15′
[(a) 0.838 (b) 1.481 (c) 4.054]
3. Convert to degrees: (a) 5π 6
rad (b) 4π 9
rad
(c) 7π 12
rad [(a) 150◦ (b) 80◦ (c) 105◦ ]
4. Convert to degrees and minutes: (a) 0.0125 rad (b) 2.69 rad (c) 7.241 rad
[(a) 0◦ 43′ (b) 154◦ 8′ (c) 414◦ 53′]
Problem 8. Find the length of arc of a circle of radius 5.5 cm when the angle subtended at the centre is 1.20 radians
From equation (1), length of arc, s = rθ, where θ is in radians, hence
s = (5.5)(1.20) = 6.60 cm
Problem 9. Determine the diameter and circumference of a circle if an arc of length 4.75 cm subtends an angle of 0.91 radians
Since s = rθ then r = s θ
= 4.75 0.91
= 5.22 cm. Diameter = 2 × radius = 2 × 5.22 = 10.44 cm. Circumference, c =πd =π(10.44) = 32.80 cm.
