Apps. and Interpretation for IBDP Maths Ebook 2 | Page 53

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Paper 1 – Composite Trigonometric Functions
Example
Let
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� x � f ( x) � x � 1, gx ( ) �5cos�
��2 . Let h( x) � ( g f )( x) .
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�2 �
( a ) Find an expression for hx ( ).
( b ) Find the period of h .
( c ) Write down the range of h .
[ 3 ]
[ 2 ]
[ 2 ]

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Solution
( a )
h( x) � g( f ( x))
( M1 ) for composite function
� f( x)
� hx ( ) �5cos �
��2 � 2
( A1 ) for substitution
�1
1� h( x) � 5cos � x �
��
2 �3
2�
A1 [ 3 ]
( b )
The period of h 1
�2�
3
( M1 ) for valid approach
6�
A1 [ 2 ]
( c )
{ y: �3 � y� 7 }.
A2 [ 2 ]
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