Question

Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)

Answer 1

x = a(1 – cosθ), y = b(θ – sinθ)
Differentiating x and y w.r.t. x, we get
`"dx"/"dθ" = a"d"/"dθ"(1 - cosθ)`
= a[0 – (– sin θ)] = a sin θ
and
`"dy"/"dθ" = b"d"/"dθ"(θ - sin θ)`
= b(1 – cos θ)
∴ `"dy"/"dx" = (("dy"/"dθ"))/(("dx"/"dθ")`

= `(b(1 - cosθ))/(asinθ)`

= `(b xx 2sin^2(θ/2))/(a xx 2sin(θ/2) cos(θ/2)`

= `(b/a)tan(θ/2)`.