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Find the equation of all lines tangent to the parametric curve $x( t ) =\sin { ( 2t ) } ,\ y( t ) =-\cos { ( t ) } +1$ at the point:

$$x=0,\quad y=1\quad$$

A

$y=\cfrac{1}{2}x+1$

B

$y=-\cfrac{1}{2}x+1$

C

$y=\cfrac{1}{2}x+1\quad \text{and}\quad y=-\cfrac{1}{2}x+1$

D

$y=2x+1\quad \text{and}\quad y=-2x+1$

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