Geometric optimisation with a trigonometric model

A right-triangle section has hypotenuse \(2\,\mathrm{units}\). A fixed region contributes \(7\,\mathrm{square\ units}\)

If the acute angle is \(u\), the two legs are \(2\sin(u)\) and \(2\cos(u)\)

The controlling angle is \(u\), where \(u=x\). The variable angle \(x\) lies in \(x\in\left[0,\frac{1}{2}\pi\right]\). All angles are measured in radians

Select the area model and then enter its two coefficients