Trigonometry

A right-angled triangular frame has hypotenuse \(6\text{ cm}\) and acute angle \(\theta\), where \(0^\circ<\theta<90^\circ\).

Let its perimeter be \(P\text{ cm}\).

1. Show that \(P=6+6\sin\theta+6\cos\theta. \)

2. Find the exact maximum perimeter and the corresponding \(\theta\).

3. Find the values of \(\theta\) when \(P=14\text{ cm}\).