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if x=2 cos t - cos 2t, y=2 sin t – sin 2t find d2y/dx2 at t=pi/2

if x=2 cos t - cos 2t, y=2 sin t – sin 2t find d2y/dx2 at t=pi/2

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
dx/dt=-2sint+2sin2t
dy/dt=2cost-2cos2t
dy/dx=(dy/dt)/(dx/dt)=(cost-cos2t)/(-sint+sin2t)
dy/dx=2sin3t/2.sint/2/2cos3t/2sint/2
=tan3t/2
d2y/dx2=d/dx(dy/dx)
=d/dt(dy/dx).dt/dx
=(3/2).sec23t/2.1/(-2sint+2sin2t)
=3/4.1/cos2(3t/2).1/(sin2t-sint)
=3/4.1/cos2(3t/2).1/2cos3t/2.sint/2
=(3/8).1/(cos33t/2.sint/2
put t= pi/2
d2y/dx2=3/8. 1/(cos3(3pi/4).sin(pi/4))
=-3/2
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

ankit singh
askIITians Faculty 614 Points
3 years ago
  1.  
    dx/dt=-2sint+2sin2t
    dy/dt=2cost-2cos2t
    dy/dx=(dy/dt)/(dx/dt)=(cost-cos2t)/(-sint+sin2t)
    dy/dx=2sin3t/2.sint/2/2cos3t/2sint/2
    =tan3t/2
    d2y/dx2=d/dx(dy/dx)
    =d/dt(dy/dx).dt/dx
    =(3/2).sec23t/2.1/(-2sint+2sin2t)
    =3/4.1/cos2(3t/2).1/(sin2t-sint)
    =3/4.1/cos2(3t/2).1/2cos3t/2.sint/2
    =(3/8).1/(cos33t/2.sint/2
    put t= pi/2
    d2y/dx2=3/8. 1/(cos3(3pi/4).sin(pi/4))
    =-3/2
    Thanks & Regards

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