1. CIRCULAR MEASURE
ARC LENGTH SECTOR AREA
By the end of the lesson you should be able to:
1. Convert degrees into radians and viceversa.
2. Recognize parts of a circle and use appropriate terminology.
3. Use prior knowledge on length of circumference and area of circle to
deduce formulae to calculate arc length and sector area.
4. Use prior knowledge on the trigonometric formula for the area of a
triangle to deduce a way to calculate the area of a segment.
5. Solve problems involving arc length, sector area and area of a
segment.

2. The unit circle

3. 2π rad = 360o
π rad = ....
rad = ......
....... rad = 270o

4. Express in radians
45o
60o
30o
To convert degrees to radians , multiply by

5. To convert radians to degrees , multiply by
Express in degrees:

6. Fill in the blanks in the following table

7. One radian is defined as the size of angle
corresponding to an arc of length 1 unit in a
circle of radius 1 unit.
1 unit
θ = 1 radian

8. diameter
A
B
O
C
D
E
O
P
Q
radius
minor sector
chord
minor segment
major arc

9. Calculate the length of the minor arc AB:
A
B
Arc length = 2 π r x θº
360º
Arc length = 2 π r x θ
2π
θ
in degrees:
in radians:
Arc length = r θ

10. Calculate the area of the minor sector AOB:
A
B
θ
in degrees:
in radians:
Sector Area = ½ r2
θ
Sector area = π r 2
x θº
360º
Sector area = π r 2
x θ
2π

11. Reminder:
A
B
C
a
b
c
Area of triangle = ½ x product any two sides x sin (included angle)
Area of a triangle
Area of triangle = ½ a b sin C

12. 30º
22º
12 cm
5 cm
Calculate the area of the triangle:
Area triangle = 15 cm2

13. How can we calculate the area of the minor segment?
Area segment = Area sector AOB ­ Area triangle AOB
Area segment =
Area segment =
A
O
B
θ

14. How can we calculate the area of the major segment?
Area segment = Area sector AOB + Area triangle AOB
Area segment =
Area segment =
A
O
B
θ

15. At end of lesson ...
Terminology Quiz
See next page ...

16. 1) The distance around the edge of a circle.
Circumference
2) The circumference of any circle divided by its diameter.
Pi
3) A portion of the circumference of a circle.
Arc
4) A straight line that links two points on a circumference.
Chord
5) A line from the center of a circle to a point on the circle.
Radius
6) Given two points on a circumference, the shortest arc linking them.
Minor arc
7) The distance along the curved line making up the arc.
Arc length
8) The area enclosed by two radii of a circle and their intercepted arc .
A pie­shaped part of a circle.
Sector
9) The region between a chord of a circle and its associated arc.
Segment

17. Attachments
Arc length and Sector area Past papers Problems.rtf