Question

If x=a (t-sint), y=a (1+cost) then find dy/dx​

Answer 1

Answer:

dx/dt = -acost ,dy/dt = -asint

then

dy/dx = (dy/dt)/(dx/dt) = -asint/(-acost) = tant

Answer 2

$x = a(t - sint) \\ \frac{dx}{dt} = a(1 - cost) \\ \\ y = a(1 + cost) \\ \frac{dy}{dt} = a( - sint) \\ \\ \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } = \frac{a( - sint)}{a(1 - cost)} \\ \\ \frac{dy}{dx} = \frac{ - 2sin \frac{t}{2} cos \frac{t}{2} }{2 {sin}^{2} \frac{t}{2} } \\ \\ \frac{dy}{dx} = - \frac{cos \frac{t}{2} }{sin \frac{t}{2} } \\ \\ \frac{dy}{dx} = cot \frac{t}{2}$