CAIE Further Paper 2 2024 June — Question 3

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2024
SessionJune
TopicParametric equations

3 It is given that $$\mathrm { x } = \sin ^ { - 1 } \mathrm { t } \quad \text { and } \quad \mathrm { y } = \mathrm { tcos } ^ { - 1 } \mathrm { t } , \quad \text { for } 0 \leqslant t < 1 .$$
  1. Show that \(\frac { d y } { d x } = - t + \sqrt { 1 - t ^ { 2 } } \cos ^ { - 1 } t\).
  2. Find \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\) in terms of \(t\).