9 . Consider the following circle with centre O and radius r .
A C
The points A , B and C are on the circumference such that π
0 ��
� . 2
AOB ˆ � 2� ,
( a ) Show that AB �r 2 ( 1� cos 2 �)
.
Let P be the perimeter of the shaded region .
( b ) Show that P�2 r( �� sin �)
.
Consider the function f ( �) �� � sin� , π
0 ��
� . 2
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( c ) Write down the value of � when
( i ) f ( �) �2 � 0 ;
( ii ) 2 f ( �) �3 � 0 .
( d ) Hence , find the range of values of � such that P lies exclusively between 1.5 to 2 times the diameter of the circle .
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