15_5_1 - 1 The polar curve r = g is parametrized by x = g...

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1. The polar curve r = g (θ ) is parametrized by x = g (θ ) cos θ, y = g (θ ) sin θ. Hence its arc length element is ds = s ± dx d θ ² 2 + ± dy d θ ² 2 d θ = q ( g 0 (θ ) cos θ - g (θ ) sin θ ) 2 + ( g 0 (θ ) sin θ + g (θ ) cos θ ) 2 d θ = q ( g (θ ) ) 2 + ( g 0 (θ )
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