| Exam Board | Edexcel |
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| Module | C3 (Core Mathematics 3) |
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| Year | 2010 |
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| Session | January |
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| Topic | Harmonic Form |
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3. (a) Express \(5 \cos x - 3 \sin x\) in the form \(R \cos ( x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
(b) Hence, or otherwise, solve the equation
$$5 \cos x - 3 \sin x = 4$$
for \(0 \leqslant x < 2 \pi\), giving your answers to 2 decimal places.