In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve $$\(C\)$$ has parametric equations $$\[ x=\sin t-3 \cos ^{2} t \quad y=3 \sin t+2 \cos t \quad 0 \leqslant t \leqslant 5 \]$$ (a) Show that $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}=3\)$$ where $$\(t=\pi\)$$ (4) The point $$\(P\)$$ lies on $$\(C\)$$ where $$\(t=\pi\)$$ (b) Find the equation of the tangent to the curve at $$\(P\)$$ in the form $$\(y=m x+c\)$$ where $$\(m\)$$ and $$\(c\)$$ are constants to be found. (3) Given that the tangent to the curve at $$\(P\)$$ cuts $$\(C\)$$ at the point $$\(Q\)$$ (c) show that the value of $$\(t\)$$ at point $$\(Q\)$$ satisfies the equation $$\[ 9 \cos ^{2} t+2 \cos t-7=0 \]$$ (2) (d) Hence find the exact value of the $$\(y\)$$ coordinate of $$\(Q\)$$ (3)

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