3.
$$g ( \theta ) = 4 \cos 2 \theta + 2 \sin 2 \theta$$
Given that \(\mathrm { g } ( \theta ) = R \cos ( 2 \theta - \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\),
- find the exact value of \(R\) and the value of \(\alpha\) to 2 decimal places.
- Hence solve, for \(- 90 ^ { \circ } < \theta < 90 ^ { \circ }\),
$$4 \cos 2 \theta + 2 \sin 2 \theta = 1$$
giving your answers to one decimal place.
Given that \(k\) is a constant and the equation \(\mathrm { g } ( \theta ) = k\) has no solutions,
- state the range of possible values of \(k\).