It is given that \( \mathrm{f}(x)=2\sin\frac{x}{2} \) and \( \mathrm{g}(x)=3\cos x+1 \), where \( 0\le x\le 2\pi \).
State the period of \( \mathrm{f}(x) \).[1]
State the smallest value of \( \mathrm{f}(x) \).[1]
State the largest value of \( \mathrm{g}(x) \).[1]
Sketch on the same axes, the graphs of \( y=\mathrm{f}(x) \) and \( y=\mathrm{g}(x) \) for \( 0\le x\le 2\pi \). Label your graphs clearly.[4]
The solutions to the equation \( \mathrm{f}(x)=\mathrm{g}(x) \) for \( 0\le x\le 2\pi \) are \( a \) and \( b \), where \( a<b \). State, in terms of \( a \) and \( b \), the range of values of \( x \) for which \( \mathrm{f}(x)>\mathrm{g}(x) \).[1]