AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED

Mathematics pure 1 (circular measure) email:racsostudenthelp@gmail.com
4.Circular measure
- What is a radian?
- A radian means 1 radian, a radian is the angel formed at the center of a circle when the radius and
arc of the circle are equal in length.
(https://www.google.co.za/search?q=radians&source)
-THE RELATIONSHIP BETWEEN RADIAN AND DEGREES
π radians = 180 degrees
π = 3.14159265….. approx. π = 3.14.
this means..
-If the blue line and red line
(radius) are equal in length
then the angle is one radian
A radius is a straight line
from the center to the
circumference of a circle or
sphere
Arch is the length of a
curved part represented by
the blue line.
3.14 radians = 180 degrees, how about 1 radian?
1radian = 180/3.14 =57.9 degrees.
What does this means? It means 1 radian = 57.29 degrees.
A book definition of a
radian: a unit of
measurement of angles
equal to about 57.3°,
equivalent to the angle
subtended at the center of
a circle by an arc equal in
length to the radius.
(https://www.google.co.za/
?gfe_rd=cr&ei=duOnU7ThK
qrd8gfa9ICIBQ&gws_rd=ssl
#q=define+radian)
-You should know how to convert degrees to radians and radians back to degrees using the relation shown above
(π radians = 180 degrees)
RACSO PRODUCTS Page 1

Note: θ is in radians.
Sector
Very important!
The formula s = r θ is find the circumference (distance) of the arch and is for A = 1/2 r2θ
finding the area of the sector
Example: If given Radius = 6 cm, and θ = π/3 . (π= 3.14)
i) Find the circumference of the arch.
ii) Find the perimeter of the sector ( hint: add perimeter of arch and the 2 x r)
iii) Find the area of the sector.

Special angles
Note: You are expected to know this table for your exam;

Let us go through past papers questions
Perimeter of the sector AOB is r.θ +2r
Perimeter of the sector BOC is r (π – θ) +2r.
If I multiple (r.θ +2r) by 2 = r (π – θ) +2r
May/June 2003 (CIE)
Part (i) – they need the formula,
calculation and a correct answer.
- A = 1/2 r2θ
R=8cm
Angle = (π – 1)
Before we solve part (iii) I urge you to note down the concept below.
-Whenever a triangle is confined in a semi-circle as the one show below, it is always a
right-angled triangle.
-You learnt this in grade 10 (circles or euclidean
geometry)

-So we now know that the angle ABC is π radians. AC= 16 cm.
-you are required to find the
perimeter of the red triangle
and show that is equal to
(24 + 8√3) cm
The distance OB and OA are
equal. OB=OA= radius=8cm.
that means triangle AOB is an
isosceles triangle. Angle B and
angle A are equal.
(You can go back and learn
the 3 types of triangle and
there properties)
θ given as π/3
Angles equal
let angle B = z which means angel A
will be z. so, z + z + π/3 = π
2z = 2 π/3 so z= π/6
Use the special angles
on previous page to
obtain tan π/3 and
We can get the distance BC
By using: AB=16 x tan π/3
And find BC= 16/ cos π/3
AC = 16.
-Therefore total perimeter is
AB +BC+AC which should be
=(24 + 8√3) cm
Note: do not change any fraction to decimal,
remember you final answer should be
=(24 + 8√3) cm.
Cos π/3
Angle = π/6 Angle = π/3

AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED

More Related Content

What's hot

Viewers also liked

Similar to AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED

More from RACSOelimu

Recently uploaded

AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED