Apps. and Interpretation for IBDP Maths Ebook 2 | Page 52

Your Practice Set – Applications and Interpretation for IBDP Mathematics

14

Paper 1 – Solving Trigonometric Equations
Example
( a ) Solve cos 2x� �3sin x� 4 for 0�x
� 6π . [ 4 ]
( b ) Write down the number of solution ( s ) of 1� cos2x� �3sin x� 4 for 0�x
� 6π . [ 1 ]
Solution
( a )
cos 2x� �3sin x�
4
cos 2x� 3sin x� 4 �
0
( M1 ) for valid approach
By considering the graph of y � cos2x �3sin x � 4
,
x � 4.7123885 , x � 10.995574 or x � 17.278759
.
�x � 4.71 , x � 11.0 or x �
17.3
A3
( b )
0
A1
[ 4 ]
[ 1 ]
Exercise 14
1 .
( a )
2 Solve 5�2cos x� 3cos x for
0�x � 4π
.
( b )
2 Write down the number of solution ( s ) of �
�2cos x� 3cos x for
0�x � 4π
.
[ 4 ]
[ 1 ]
2 . ( a ) Solve cos 2x� 4� 7sin x for 0�x
� 2π . [ 3 ]
( b ) Write down the number of solution ( s ) of cos2x�2 �4� 7sin x for 0�x
� 2π . [ 1 ]
3 . ( a ) Solve sin x �sin xcos x � 0, for 0�x
� 4π .
( b ) Write down the number of solution ( s ) of sin x sin xcos x 0
[ 3 ]
�
�
for �5π � x � π
.
[ 1 ]
4 .
( a )
� Solve cos 2x�sin 4x� 0, for 0 � x �
.
2
( b )
Write down the number of solution ( s ) of cos2x�sin 4x� 0 for �2π � x
� � π.
[ 3 ] [ 1 ]
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