Find angle \(A B C\).
The point \(D\) is such that \(A B C D\) is a parallelogram.
Find the position vector of \(D\).
9 The function f is such that \(\mathrm { f } ( x ) = 3 - 4 \cos ^ { k } x\), for \(0 \leqslant x \leqslant \pi\), where \(k\) is a constant.
In the case where \(k = 2\),
(a) find the range of f,
(b) find the exact solutions of the equation \(\mathrm { f } ( x ) = 1\).
In the case where \(k = 1\),
(a) sketch the graph of \(y = \mathrm { f } ( x )\),
(b) state, with a reason, whether f has an inverse.
10 (a) A circle is divided into 6 sectors in such a way that the angles of the sectors are in arithmetic progression. The angle of the largest sector is 4 times the angle of the smallest sector. Given that the radius of the circle is 5 cm , find the perimeter of the smallest sector.
(b) The first, second and third terms of a geometric progression are \(2 k + 3 , k + 6\) and \(k\), respectively. Given that all the terms of the geometric progression are positive, calculate