Question

有哪位高数大神，帮我解一下，谢谢了

Answer 1

x=a(t-sint)
dx/dt = a(1-cost)
y=a(1-cost)
dy/dt = asint
-------
dy/dx
=(dy/dt)/(dx/dt)
=sint/(1-cost)
=sint(1+cost)/[1-(cost)^2]
= (1+cost)/sint
=csct + cot(t)
d^2y/dx^2
=d/dt ( dy/dx)/ (dx/dt)
= [-csct.cot(t) - (csct)^2 ] /[a(1-cost)]
={ -cost/(sint)^2 - 1/(sint)^2 } /[a(1-cost)]
= -(1+cost)^2/[a(sint)^4]