AS June 2020 Paper 1 Q11
11 Sketch the polar graph of
\[r = \sinh\theta + \cosh\theta\]for \(0 \leqslant \theta \leqslant 2\pi\) [3 marks]
| Scheme | Marks | AO |
|---|---|---|
| Selects an approach to sketch the polar graph of \(r = \sinh\theta + \cosh\theta\) e.g. by evaluating \(r\) for at least 3 values of \(\theta\) PI or by finding \(\sinh\theta + \cosh\theta = \mathrm{e}^\theta\). | M1 | 3.1a |
| Draws a spiral. | M1 | 1.1a |
| Completes a fully correct sketch with the spiral beginning and ending on the initial line (not at the pole.) | A1 | 1.1b |
| (3 marks) |
Typical solution
\[\sinh\theta + \cosh\theta = \mathrm{e}^\theta\]