2022 TJC J2 MYE P1 Q2
2022 TJC J2 MYE P1 Q2
5 marks
Mid Year Exam
By expressing \(\sin 3x-\cos 3x\) in the form \(R\sin \left( 3x-\alpha \right)\), where \(R>0\) and \(0<\alpha <\frac{\pi }{2}\), describe a sequence of transformations that will transform the graph of \(y=\sin x\) onto the graph of \(y=\sin 3x-\cos 3x\).[5]
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Answer:\(\sqrt{2}\sin\left(3x - \displaystyle\frac{\pi}{4}\right)\); Transformations: (I) Translate \(\displaystyle\frac{\pi}{4}\) in positive x-direction; (II) Scale parallel to x-axis by factor \(\displaystyle\frac{1}{3}\); (III) Scale parallel to y-axis by factor \(\sqrt{2}\)
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