A curve is defined by the parametric equations $$\[ x=3 t-2 \sin t, \quad y=5 t+4 \cos t, \]$$ where $$\(0 \leqslant t \leqslant 2 \pi\)$$. At each of the points $$\(P\)$$ and $$\(Q\)$$ on the curve, the gradient of the curve is $$\(\frac{5}{2}\)$$. Express $$\(10 \cos t-8 \sin t\)$$ in the form $$\(R \cos (t+\alpha)\)$$, where $$\(R>0\)$$ and $$\(0<\alpha<\frac{1}{2} \pi\)$$. Give the exact value of $$\(R\)$$ and the value of $$\(\alpha\)$$ correct to 3 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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