CAIE Further Paper 2 2020 November — Question 5

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

5 It is given that $$x = \sinh ^ { - 1 } t , \quad y = \cos ^ { - 1 } t$$ where \(- 1 < t < 1\).
  1. By differentiating \(\cos y\) with respect to \(t\), show that \(\frac { d y } { d t } = - \frac { 1 } { \sqrt { 1 - t ^ { 2 } } }\).
  2. Find \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\) in terms of \(t\), simplifying your answer.