WJEC Further Unit 4 2022 June — Question 13

Exam BoardWJEC
ModuleFurther Unit 4 (Further Unit 4)
Year2022
SessionJune
TopicPolar coordinates

13. The curve \(C\) has polar equation \(r = 2 - \cos \theta\) for \(0 \leqslant \theta \leqslant 2 \pi\).
  1. Sketch the curve \(C\).
    1. Show that the values of \(\theta\) at which the tangent to the curve \(r = 2 - \cos \theta\) is parallel to the initial line satisfy the equation $$2 \cos ^ { 2 } \theta - 2 \cos \theta - 1 = 0$$
    2. Find the polar coordinates of the points where the tangent to the curve \(r = 2 - \cos \theta\) is parallel to the initial line.