In earlier work, angles were measured in degrees where 1° = 
of one revolution. i.e. 360° = one revolution.
This is not a particularly useful way of measuring angles as most formulae for circles use π.
Other ways of measuring angle size are radians(see below) and grads, which will not be studied further.
(1 gradian or grad = 1/100 of a right angle or 0.9 of a degree.)
Students should be familiar with both degrees and radians as a means of measuring angles.
Make sure that calculators are set to the mode of angle measurement required.
Radians
A radian is defined as the angle made at the centre of a circle, of radius r, by an arc of length r.
e.g.
This would be true for every circle regardless of size.
The circumference of a circle = 2π r therefore an angle of 360° = 2π r ÷ r = 2π radians
Changing Degrees to Radians
2π radians radians
radians
To change Degrees to Radians multiply by Changing Radians to Degrees
360° °
°
To change Radians to Degrees multiply by
Length of an Arc
The length of an arc of a circle can now be calculated. An arc is said to be minor if the angle subtended at the centre is less than 180°.
Area of a Sector
The area of a sector of a circle can also be found. A sector is said to be minor if the angle subtended at the centre is less than 180°
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Example of Length of Arc
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Example of Area of Sector
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Find the length of arc AB
Angle is already in radians. Length of arc = r θ = 7.8 x 7π/8 = 21.4 mm (to 3 sig.fig.) |
Find the area of sector AOB.
First change angle from degrees to radians. 125° = 125 x Area of sector AOB = 0.5 x r 2 θ = 0.5 x 62 x 2.18 = 39.2 cm2 (to 3 sig. fig.) |
= 2.18 radians (to 3 sig. fig.)
