Question

x=acos∧4t y=bsin∧4t dy/dx at t=3pi/4

Answer 1

Answer:

Please see the attachment

Answer 2

The value of dy/dx at t = 3π/4 is - b / a.

Given: x = a cos^4 t and y = b sin^4 t

To Find: dy/dx at t = 3π/4

Solution:

    x = a cos^4 t  

⇒ dx/dt = - 4a cos³ t . sin t

   y = b sin^4 t

⇒ dy/dt = 4b sin³ t . cos t

dy/dx = dy/dt ÷ dx/dt

          = 4b sin³ t . cos t / ( - 4a cos³ t . sin t )

          = - ( b / a ) × tan² t                                            .......(1)

Now at t = 3π/4, we put the values in (1), we get;

          = - ( b / a ) × tan² 3π/4

          = - ( b / a ) × (-1)²                                  [ as tan 3π/4 = - 1 ]

          = - b / a

Hence, the value of dy/dx at t = 3π/4 is - b / a.

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