Figure 3 shows a sketch of the curve $$\(C\)$$ with parametric equations $$\[ x=1+3 \tan t \quad y=2 \cos 2 t \quad-\frac{\pi}{6} \leqslant t \leqslant \frac{\pi}{3} \]$$ The curve crosses the $$\(x\)$$-axis at point $$\(P\)$$, as shown in Figure 3. (a) Find the equation of the tangent to $$\(C\)$$ at $$\(P\)$$, writing your answer in the form $$\(y=m x+c\)$$, where $$\(m\)$$ and $$\(c\)$$ are constants to be found. (5) The curve $$\(C\)$$ has equation $$\(y=\mathrm{f}(x)\)$$, where $$\(\mathrm{f}\)$$ is a function with domain $$\([k, 1+3 \sqrt{3}]\)$$ (b) Find the exact value of the constant $$\(k\)$$. (1) (c) Find the range of $$\(f\)$$. (2)

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