OCR FP2 2008 January — Question 2

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionJanuary
TopicReciprocal Trig & Identities

2
\includegraphics[max width=\textwidth, alt={}, center]{15dd10f9-73d4-4107-bb45-7866f5470572-2_577_700_577_721} The diagram shows parts of the curves with equations \(y = \cos ^ { - 1 } x\) and \(y = \frac { 1 } { 2 } \sin ^ { - 1 } x\), and their point of intersection \(P\).
  1. Verify that the coordinates of \(P\) are \(\left( \frac { 1 } { 2 } \sqrt { 3 } , \frac { 1 } { 6 } \pi \right)\).
  2. Find the gradient of each curve at \(P\).