Find d^2 y/dx^2 for the curve given by. x=2 cos theta and y=sin theta

Nelson Jennings 2022-07-28 Answered
Find d 2 y / d x 2 for the curve given by x = 2 cos θ   a n d   y = sin θ
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Answers (1)

Hassan Watkins
Answered 2022-07-29 Author has 18 answers
cos ( θ ) = x 2
sin ( θ ) = y
cos 2 ( θ ) + sin 2 ( θ ) = 1
( x 2 ) 2 + y 2 = 1
x 2 + 4 y 2 = 4 [equation of curve]
Differentiating both sides with respect to x,
2 x + 4 × ( 2 y d y d x ) = 0
d y d x = x 4 y
d d x ( d y d x ) = d d x ( x 4 y )
d 2 y d x 2 = y × 1 x × d y d x 4 y 2
Now, put value of dy/dx.
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