June 2018 Paper 2 Q13

(a) Here is a sketch of \(\ y = \tan x\ \) for \(\ 0^\circ \leqslant x \leqslant 360^\circ\)

How many solutions of \(\ \tan x = k\ \) where \(k \gt 0\) are between \(90^\circ\) and \(360^\circ\)? [1 mark]

(b) \(0 \lt p \lt 1\)

How many solutions of \(\ \sin x = p - 1\ \) are between \(0^\circ\) and \(180^\circ\)?

You may use a sketch graph to help you. [1 mark]

(c) State the coordinates of each point where the graph

\(y = \cos x \qquad\) for \(\ 0^\circ \leqslant x \leqslant 360^\circ\)

meets or intersects an axis. [2 marks]