4.
$$f ( x ) = 8 \sin x \cos x + 4 \cos ^ { 2 } x - 3$$
- Write \(\mathrm { f } ( x )\) in the form
$$a \sin 2 x + b \cos 2 x + c$$
where \(a\), \(b\) and \(c\) are integers to be found.
- Use the answer to part (a) to write \(\mathrm { f } ( x )\) in the form
$$R \sin ( 2 x + \alpha ) + c$$
where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\)
Give the exact value of \(R\) and give the value of \(\alpha\) in radians to 3 significant figures. - Hence, or otherwise,
- state the maximum value of \(\mathrm { f } ( x )\)
- find the second smallest positive value of \(x\) at which a maximum value of \(\mathrm { f } ( x )\) occurs. Give your answer to 3 significant figures.