If x=asinpt and y=bcospt, find the value of d2y/dx2 at t=0.
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x = asinpt
differentiate wrt t
dx/dt = apcospt -------------(1)
again,
y =bcospt
differentiate wrt t
dy/dt = -bpsinpt ------------(2)
divide equation (2) by (1)
dy/dx = -(b/a)tanpt
differentiate wrt x
d²y/dx² = -p(b/a)sec²pt.dt/dx
put dx/dt = apcospt
dt/dx =1/ap secpt
d²y/dx² = -p(b/a)(1/ap)sec³pt
put t =0
then, d²y/dx² = -b/a²
differentiate wrt t
dx/dt = apcospt -------------(1)
again,
y =bcospt
differentiate wrt t
dy/dt = -bpsinpt ------------(2)
divide equation (2) by (1)
dy/dx = -(b/a)tanpt
differentiate wrt x
d²y/dx² = -p(b/a)sec²pt.dt/dx
put dx/dt = apcospt
dt/dx =1/ap secpt
d²y/dx² = -p(b/a)(1/ap)sec³pt
put t =0
then, d²y/dx² = -b/a²
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