8.
$$f ( x ) = 2 x + \sin x - 3 \cos x$$
- Show that the equation \(\mathrm { f } ( x ) = 0\) has a root in the interval [0.7, 0.8].
- Find an equation for the tangent to the curve \(y = \mathrm { f } ( x )\) at the point where it crosses the \(y\)-axis.
- Find the values of the constants \(a , b\) and \(c\), where \(b > 0\) and \(0 < c < \frac { \pi } { 2 }\), such that
$$f ^ { \prime } ( x ) = a + b \cos ( x - c )$$
- Hence find the \(x\)-coordinates of the stationary points of the curve \(y = \mathrm { f } ( x )\) in the interval \(0 \leq x \leq 2 \pi\), giving your answers to 2 decimal places.