1.07i Differentiate x^n: for rational n and sums

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Pre-U Pre-U 9795/1 2013 November Q5
8 marks Challenging +1.2
The curve \(S\) has polar equation \(r = 1 + \sin \theta + \sin^2 \theta\) for \(0 \leqslant \theta < 2\pi\).
  1. Determine the polar coordinates of the points on \(S\) where \(\frac{dr}{d\theta} = 0\). [5]
  2. Sketch \(S\). [3]