4. $$\mathrm { f } ( x ) = 12 \cos x - 4 \sin x$$ Given that \(\mathrm { f } ( x ) = R \cos ( x + \alpha )\), where \(R \geqslant 0\) and \(0 \leqslant \alpha \leqslant 90 ^ { \circ }\),

1. find the value of \(R\) and the value of \(\alpha\).
   (4)
2. Hence solve the equation $$12 \cos x - 4 \sin x = 7$$ for \(0 \leqslant x < 360 ^ { \circ }\), giving your answers to one decimal place.
3. 1. Write down the minimum value of \(12 \cos x - 4 \sin x\).
   2. Find, to 2 decimal places, the smallest positive value of \(x\) for which this minimum value occurs.
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