Analysis and Approaches for IBDP Maths Ebook 2 | Page 288

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 37
37.1 (a)
3 4
z � � i
5 5
(b) 1
(c) 0.927 rad
37.2
37.3
* 2
( � ) 2 1 cos
� � � ,
* 2
arg(( � ) )
��
� � i
2
� � �
� 2 �
(1 ��) � 2 1�
sin�
e
37.4 (a) a � 3
(b) z1 � 2
(c)
Exercise 38
z
�
i
6
2
� 2e
38.1 (a) Refer to solution
(b) 12
(c) 2 and 6
38.2 a � 4 , b � 1
38.3 a � 5 , b � 2
38.4 a � 2 , b � 3
Exercise 39
39.1 (a) (i)
(ii)
cos
4
�
3
�4i cos � sin�
2 2
�6cos
�sin
�
3
�4i cos�
sin �
4
� sin �
4
cos 4�
� cos �
2 2
�6cos
�sin
� ,
4
�sin
�
� �
3
sin 4 � 4cos sin
� � �
3
�4cos�sin
�
3�
(b) r � 2,
� �
8
(c)
3�
2 � 2
cos � 8 4
39.2 (a)
8cos
7
�sin�
5 3
�56 cos � sin �
3 5
�56 cos � sin �
7
�8cos�sin
�
(b)
�
r � 3, �1
��
8
(c) Refer to solution
(d) (i) 3
(ii) Rectangle
(iii) Trapezium
(iv) BE � 5.54
39.3 (a) Refer to solution
(b)
8 6 2
cos � � 28cos � sin �
4 4
�70 cos � sin �
2 6 8
�28cos � sin � �sin
�
(c)
�
� � 0.187 or � �
4
5 �
cos�
� cos 5
39.4 (a)
3�
2�
�10 cos sin ,
5 5
� 4 �
�5cos
sin
5 5
4 � �
sin�
� 5cos sin
5 5
2 � 3 � 5 �
�10 cos sin � sin
5 5 5
(b) Refer to solution
(c)
� 2�
x � tan , x � tan ,
5 5
3�
4�
x � tan or x � tan 5
5
(d)
(i)
(ii)
4
�
r�0
r�
tan � 0
5
� 2� tan tan � 5
5 5
(d)
Refer to solution
278
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