Analysis and Approaches for IBDP Maths Ebook 2 | Page 187

(f)
�
� cot � ( �cot 2 �a) � 1
2
cot 2� a � 1
A1
tan 2�
a � 1
�
2� a � M1
4
1
a � A1
8
3
b �� ,
8
1
b �� A2
8
[8]
[2]
13
Exercise 57
1. Consider the function f ( x) � sec�
x ,
� � �
x
2�
� � 2�
. The period of f is 8� .
(a)
(b)
Show that
1
� � .
4
Show that f is an even function.
(c) (i) State the largest possible domain of f such that
1
f �
exists.
[2]
[2]
(ii)
Under this restriction, find the expression of
The region bounded by the curve
1
f � .
y� sec�
x and the lines x� a and x �� � , where
0�a
� 2�
, is rotated through 2π radians about the x -axis. The volume of the solid
generated is 4 � ( 3 � 1) .
[5]
(d) Find the value of a , giving the answer in terms of � .
[8]
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