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Question
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)
Solution
x = a `(cos theta + theta sin theta)`, y = a `(sin theta - theta cos theta)`
`dx/(d theta) = a [- sin theta + theta * cos theta + sin theta]`
`= a theta cos theta`
`dy/(d theta) = a [cos theta - (theta(-sin theta) + cos theta)]`
= a [cos θ + θ sin θ - cos θ]
= a θ sin θ
`dy/dx = (dy/(dθ))/(dx/(dθ))`
`= (a θ sin θ)/ (a θ cos θ)`
= tan θ
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