A system of equations is given by

\[\cos x + \cos y = 1.2\]

\[\sin x + \sin y = 1.4{\text{ .}}\]

(a)     For each equation express y in terms of x.

(b)     Hence solve the system for \(0 < x < \pi ,{\text{ }}0 < y < \pi \) .

(a)     \(y = \arccos (1.2 - \cos x)\)     A1

\(y = \arcsin (1.4 - \sin x)\)     A1

(b)     The solutions are

x = 1.26, y = 0.464     A1A1

x = 0.464, y = 1.26     A1A1

[6 marks]

The majority of candidates obtained the first two marks. Candidates who used their GDC to solve this question did so successfully, although few candidates provided a sketch as the rubric requires. Attempts to use “solver” only gave one solution.

Some candidates did not give the solutions as coordinate pairs, but simply stated the x and y values.