Hello,
[tex]x=cos(t)==\ \textgreater \ \dfrac{dx}{dt} =-sin(t)\\
y= \dfrac{sin(2t)}{2}==\ \textgreater \ \dfrac{dy}{dt} =cos(2t)\\
\dfrac{dy}{dx} = \dfrac{ \frac{dy}{dt}}{ \frac{dx}{dt} } =- \frac{cos(2t)}{sin(t)} \\
For\ x=0, \ t=cos(0)= \frac{ \pi }{2} +k \pi \\
( \dfrac{dy}{dx} )_{x=0} =\pm\ 1\\
tangents \ are\ \{ y=-x,y=x \}\\
[/tex]
