1. Radian Measure
Gamma maths chapter33 radians to degrees, degrees to radians, angle and sector area

2. Calculate the area of the dark part of his circle.
The radius is 12.5 m long.
m2 (1dp)

3. Two sectors have the same centre angle
1 radian = the angle formed in a sector with the arc
length the same as the radius
1 radian
The length of an arc is proportional to both:
The angle at the centre of the arc
The radius of the arc
Two sectors have the same radius
Two sectors have the same centre angle
Θ s θ s
r r
Θ s
2θ s

4. Arc Length Formula s = rθ s s = arc length r = length of radius
Θ = angle at centre of sector,
measured in radians θ r r
Rearranging the arc length formula, we have:
angle = arc length or θ = s
radius r

5. Conversion of degrees/radians00
3600 2π π
1800
3600 = 2 π so = π
To convert degrees to radians, multiply by
To convert radians to degrees, multiply by

6. Convert 450 to radians. Leave your answer in terms of π
450 = 45 x = x π = x π =
Convert radians to degrees.
Answer
= 2 x = = 1200
Using the arc length formula calculate the length of the arc ABC
s = rθ so ABC = rθ
= 8 x
= cm
or in decimal form 20.1 cm (1dp) B A
8 cm C
8 cm

7. Calculate the size of the angle labelled θ in degrees.6 5 θ 5

8. Sector area formula Area A = ½ r2 θ (note θ is in radians) Answer Π
The angle at the centre of the shaded sector is
2π =
Area of sector = ½ x 22 x
= cm2
or cm2 (4sf) Π 3
2 cm
2 cm
The sector area formula can be rearranged to make either θ or r the subject
2A = r2θ
Θ = r =

9. Area of Segment Your calculator must be set in radians
The Area of a Segment is the
area of a sector minus the
triangular piece.
Your calculator must be set in radians
Area of Segment = ½ × (θ - sin θ) × r2
= ½ × ( (θ × π/180) - sin θ) × r2   (if θ is in degrees)