OCR Further Pure Core 2 2022 June — Question 2

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2022
SessionJune
TopicPolar coordinates

2 Two polar curves, \(C _ { 1 }\) and \(C _ { 2 }\), are defined by \(C _ { 1 } : r = 2 \theta\) and \(C _ { 2 } : r = \theta + 1\) where \(0 \leqslant \theta \leqslant 2 \pi\). \(C _ { 1 }\) intersects the initial line at two points, the pole and the point \(A\).
  1. Write down the polar coordinates of \(A\).
  2. Determine the polar coordinates of the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\). The diagram below shows a sketch of \(C _ { 1 }\).
    \includegraphics[max width=\textwidth, alt={}, center]{007f07ee-cb29-4a97-93d9-2328079c4aea-2_681_1353_1318_244}
  3. On the copy of this sketch in the Printed Answer Booklet, sketch \(C _ { 2 }\).