Candidates should be able to:

• understand the relations between cartesian and polar coordinates (using the convention \(r \geqslant 0\)), and convert equations of curves from cartesian to polar form and vice versa;
• sketch simple polar curves, for \(0 \leqslant \theta < 2\pi\) or \(−\pi < \theta \leqslant \pi\) or a subset of either of these intervals (detailed plotting of curves will not be required, but sketches will generally be expected to show significant features, such as symmetry, the form of the curve at the pole and least/greatest values of r);
• recall the formula \(\int^{\beta}_{\alpha} r^2 d\theta\) for the area of a sector, and use this formula in simple cases.

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Polar coordinates – Further Pure Maths 1 Video (1:58:58)

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