12 . The functions f and g are defined as f ( y) � asin 2� y and g( y) �� sin� y respectively , a � 0 , 0� y � 1. Let P ( f ( r), r ) be the point of intersection of the graphs of f and g .
( a ) Consider the case when a � 1.
( i ) Show that
2 r � .
3
( ii ) Hence , show that the area of the region bounded by graph of f , the graph of g and the lines y
� r and y � 1 is 1
4� . [ 9 ]
( b ) Find the value of a if the graph of f passes through
2
1 4a
�1 ( c ) Show that r � arcsin .
2
� 4a
� 2 3� Q � ,
.
� 2 4�
� � [ 3 ]
[ 9 ]
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