Exercise 46
1 . The following diagram shows a semicircle with centre O , diameter AB and radius 4 . Let
C be a point on the circumference with BOC ˆ � � radians , where 0 �� � � . Let P be the area of the triangle ABC .
( a ) ( i ) Write down the value of ˆ AOC .
( ii ) Hence , by using sin ( � ��) � sin�
, express P in terms of � .
( b ) ( i ) Write down d P
d� .
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( ii ) Solve the equation d P
0 d� � .
( iii ) Hence , find the value of � when P is at a local maximum , justifying that it is a maximum .
( iv ) Using ( a )( ii ) and ( b )( iii ) to find the maximum value of P .
( c ) Write down the two values of � for which P has its least value .
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