2.
$$f ( x ) = \cos x + 2 \sin x$$
- Express \(\mathrm { f } ( x )\) in the form \(R \cos ( x - \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\)
Give the exact value of \(R\) and give the value of \(\alpha\), in radians, to 3 decimal places.
$$g ( x ) = 3 - 7 f ( 2 x )$$ - Using the answer to part (a),
- write down the exact maximum value of \(\mathrm { g } ( x )\),
- find the smallest positive value of \(x\) for which this maximum value occurs, giving your answer to 2 decimal places.