7 The parametric equations of a curve are
$$x = 2 t - \sin 2 t , \quad y = 5 t + \cos 2 t$$
for \(0 \leqslant t \leqslant \frac { 1 } { 2 } \pi\). At the point \(P\) on the curve, the gradient of the curve is 2 .
- Show that the value of the parameter at \(P\) satisfies the equation \(2 \sin 2 t - 4 \cos 2 t = 1\).
- By first expressing \(2 \sin 2 t - 4 \cos 2 t\) in the form \(R \sin ( 2 t - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\), find the coordinates of \(P\). Give each coordinate correct to 3 significant figures.
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