Radians

Question 1

A circle has a radius r cm and a centre O.
The minor arc AB has length l cm and subtends an angle theta radians at O.
For each of the following , find the perimeter of the minor sector OAB, given:

a ) r = 0.7, theta = 2

b ) r = 4.4, theta = 0.25

Answer 1

a )

• Equation of arc length ( l ) = theta( r )
• 2 x 0.7 = 1.4 cm
• Perimeter = 2r + l
• = 2( 0.7 ) + 1.4
• = 2.8 cm

b )

• Arc length = 0.25 x 4.4
• = 1.1 cm
• Perimeter = 2( 4.4 ) + 1.1
• = 9.9 cm

Question 2

The diagram to the right shows CAB, a sector of a circle with radius 5 cm.
Find the area of the segment labelled S, giving your answer to 3 significant figures.

( Diagram shows a section of the circle )
( The points at the circumference of the circle are A and B )
( C is the point where the angle pi / 3 is )
( Radius = 5 cm )

Answer 2

• r = 5 cm
• theta = pi / 3
• Area of segment CAB = 1 /2 r^2( theta )
• = 1 / 2 ( 5 )^2 ( pi / 3 )
• = 25pi / 6
• Area of triangle ABC = 1 / 2 absin c
• = 1 /2 ( 5 ) ( 5 ) sin ( pi / 3 )
• = 25 root ( 3 ) / 4
• Area of segment = Area of sector - Area of triangle
• = 25pi / 6 - 25 root ( 3 ) / 4
• = 2.26 cm^2