| Exam Board | Edexcel |
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| Module | C3 (Core Mathematics 3) |
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| Topic | Addition & Double Angle Formulae |
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16. (a) Express \(1.5 \sin 2 x + 2 \cos 2 x\) in the form \(R \sin ( 2 x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\), giving your values of \(R\) and \(\alpha\) to 3 decimal places where appropriate.
(b) Express \(3 \sin x \cos x + 4 \cos ^ { 2 } x\) in the form \(a \cos 2 x + b \sin 2 x + c\), where \(a , b\) and \(c\) are constants to be found.
(c) Hence, using your answer to part (a), deduce the maximum value of \(3 \sin x \cos x + 4 \cos ^ { 2 } x\).