Question
\begin{aligned}&\text { If } x=a(1-\cos \theta), y=a(\theta+\sin \theta) \text {, prove that }\\&\frac{d^{2} y}{d x^{2}}=-\frac{1}{a} \text { at } \theta=\frac{\pi}{2} .\end{aligned}
Step 1
We can do this by using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, we have: \[\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta}\] Show more…
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If $x=a(1-\cos \theta), y=a(\theta+\sin \theta)$, prove that $\frac{d^{2} y}{d x^{2}}=-\frac{1}{a}$ at $\theta=\frac{\pi}{2}$
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