Analysis and Approaches for IBDP Maths Ebook 2 | Page 278

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Consider the case when n � 4 .
2
(2) Show that d4
� .
2
Consider the case when n � 5.
(3) Sketch the polygon P0 P1 P2P 3P 4
.
(4) Write down a formula for d
5
.
�
(5) Hence, show that d n
� cos .
n
�
Let A
n
be the area of the polygon P0 PP
1 2
P n� 1
, n � 3, n� .
[10]
(c) (1) By considering the angle ˆ
3 3
P0OP 1, show that A3
� .
4
(2) Find A
4
.
(3) Hence, show that
(d) Express A
n
in terms of d
n
.
A
n
n 2�
� sin .
2 n
[7]
[2]
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