CAIE P1 2017 June — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionJune
TopicTrig Graphs & Exact Values

5 The equation of a curve is \(y = 2 \cos x\).
  1. Sketch the graph of \(y = 2 \cos x\) for \(- \pi \leqslant x \leqslant \pi\), stating the coordinates of the point of intersection with the \(y\)-axis. Points \(P\) and \(Q\) lie on the curve and have \(x\)-coordinates of \(\frac { 1 } { 3 } \pi\) and \(\pi\) respectively.
  2. Find the length of \(P Q\) correct to 1 decimal place.
    The line through \(P\) and \(Q\) meets the \(x\)-axis at \(H ( h , 0 )\) and the \(y\)-axis at \(K ( 0 , k )\).
  3. Show that \(h = \frac { 5 } { 9 } \pi\) and find the value of \(k\).