Analysis and Approaches for IBDP Maths Ebook 1 | Page 104

Your Practice Set – Analysis and Approaches for IBDP Mathematics
35
Paper 1 Section A – Solving trigonometric equations
Example
Solve
Solution
� � � � � , for 0�x
� 2π .
2 2
cos 2x cos x sin x 3sin x 3
[7]
2 2
cos 2x � cos x � � sin x � 3sin x � 3
2 2 2
1� 2sin x � cos x � �sin x �3sin x � 3
(M1) for using identity
2 2 2
1� 2sin x �1�sin x � �sin x �3sin x � 3
(M1) for using identity
2
�2sin x�3sin x�5 � 0
A1
2
2sin x�3sin x�5 � 0
(sin x�1)(2sin x�5) � 0
(M1)A1 for factorization
sin x �1� 0 or 2sin x �5 � 0
A1
5
sin x �� 1 or sin x � (Rejected)
2
3�
x �
2
A1 N4
[7]
Exercise 35
1. Solve
2 2
cos 2x � cos x � 3cos x � 3� sin x , for 0 �x
� π .
[6]
2. Solve cos 2x� 7sin x� 4 � 0 , for 0�x
� 2π .
3. Solve 2sin x� sin 2x, for 0�x
� 4π .
4.
�
Solve cos2x� sin 4x, for 0 � x � .
2
[7]
[7]
[7]
96
SE Production Limited