Question

x = a(θ – sinθ), y = a(1 + cosθ) find dy/dx

Answer 1

dy/dx = -Cot(θ/2) , x = a(θ – sinθ), y = a(1 + cosθ)

Step-by-step explanation:

dy/dx

x = a(θ – sinθ)

y = a(1 + cosθ)

x = a(θ – sinθ)

dx/dθ  = a(1 – Cosθ)

y = a(1 + cosθ)

dy/dθ  = a(0 - Sinθ)

dy/dθ  =  -aSinθ

(dy/dθ)/(dx/dθ)  =   -aSinθ/a(1 – Cosθ)

=> dy/dx = -Sinθ/(1 – Cosθ)

dy/dx = -2Sin(θ/2)Cos(θ/2)/2Sin²(θ/2)

dy/dx = -Cot(θ/2)

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