CAIE Further Paper 2 2020 June — Question 5

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2020
SessionJune
TopicHyperbolic functions

5 The curves \(C _ { 1 } : y = \cosh x\) and \(C _ { 2 } : y = \sinh 2 x\) intersect at the point where \(x = a\).
  1. Find the exact value of \(a\), giving your answer in logarithmic form.
  2. Sketch \(C _ { 1 }\) and \(C _ { 2 }\) on the same diagram.
  3. Find the exact value of the length of the arc of \(C _ { 1 }\) from \(x = 0\) to \(\mathrm { x } = \mathrm { a }\).