The parametric equations of a cycloid are [tex] x=a(\theta - \sin\theta) \mbox{ and } y = a(1-\cos\theta) \\[/tex] Where a is a constant. Show that s^2=8ay, where s is the arc length measured from the point theta =0(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{dx}{d\theta} =a(1-\cos\theta) \mbox{ and } \frac{dy}{d\theta}= a\sin\theta\\ [/tex]

[tex] \int\sqrt{a^2(1-\cos\theta)^2 +a^2\sin^2 \theta}d\theta \\ = \sqrt{2}a\int\sqrt{1 - \cos\theta}d\theta\\[/tex]. I don't know how to do the integration, a hint would be welcome. Thanks.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Cycloid question

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