Find `(dy)/(dx)` , when `x=a(theta+sintheta)` and `y=a(1-costheta)`

Explanation

We can write `dy/dx`as

`frac{d y}{d x}=frac{d y}{d x} times frac{d theta}{d theta}`

`frac{d y}{d x}=frac{d y}{d theta} times frac{d theta}{d x}`

`frac{d y}{d x}=frac{frac{d y}{d theta}}{frac{d x}{d theta}}`

Calculate`frac{d y}{d theta}`

`y=a(1-cos theta)`

`frac{d y}{d theta}=frac{d(a(1-cos theta))}{d theta}`

`frac{d y}{d theta}=a(0-(-sin theta))`

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