Radians Arcs and Sectors DP

7/21/2019 Radians Arcs and Sectors DP

1/8

Radians, arcs and secto


2/8

A radian is another measure of turn. It is useful as it measures the angle in

of the arc length. Relating these two measurements can be more useful for

scientists.

The term radian comes from the word radius referring to the fixed distance

any point on the circumference of a circle to its centre. Hence 1 radian isdefined as the angle that subtends an arc length equal to the radius.

r

r

An arc length of 1 subtends a

radians, so the circumferenc

2subtends an angle of 2r

Therefore 360 = 2radia


3/8

To convert degrees to radians, multiply

To convert degrees to radians, multiply


4/8

We know that 360 = 2radians (or 2)

So when converting some angles we can write them as a fraction or mu

360 = 2radians

180 = radians

90 =

radians

60 =

6

=

3

radians

Try to keep to exact values where possible. If not then round to 3 signific


5/8

Arc length =

2

=

Area of sector =

=

Any central angle in a circle is a fraction of 2,so you can calculate the leng

arc the angle subtends as a fraction of the circumference.

Similarly the formula for the area of a circle is: Area = . The area of a se

central angle will be a fraction of the area of the circle

Remember when using these formulae the angles need to be given in ra


6/8

An arc AB subtends an angle of 2.4 radians a

centre O of a circle with radius 50cm. Find t

area and perimeter of sector AOB.

EXAMPLE


7/8

EXAM STYLE QUESTION

In the circle with centre P, the arc QR sub

an angle of at the centre. If the length o

QR is 27.2cm and the area of sector PQR

217.6cm, find and the radius of the cir


8/8

EXAM STYLE QUESTION

Circle O has radius 4cm, and circle P has radius 6cm. The

of the circles are 8cm apart. If the circles intersect at A a

find the blue shaded area in the diagram

A

B

O P

Radians Arcs and Sectors DP

Documents

Transcript of Radians Arcs and Sectors DP