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Question
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)
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Solution
Here x = a (cos θ + θ sin θ) ...(1)
y = y = a (sin θ – θ cos θ) ...(2)
Differentiating (1) and (2) w.r.t. θ, we get
`dx/(d θ)` = a [−sin θ + θ × cos θ + sin θ]
= a θ cos θ
`dy/(d theta)` = a [cos θ − (θ (−sin θ) + cos θ)]
= 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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