Parametric Curves: Finding Tangents at (0,0) Using Lissajous Figure Equations

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The discussion focuses on finding the equations of the tangents to a Lissajous figure at the origin (0,0) using the parametric equations x=sin(2t) and y=cos(t). The user has calculated the slope of the tangent as -sin(t)/cos(2t)*2 but is uncertain about the next steps. It is noted that the origin is reached when t equals π/2 and -π/2, yielding two distinct slopes of 1/2 and -1/2. The conversation emphasizes the need for clarity in deriving the tangent equations from these slopes. Overall, assistance is sought to resolve the problem effectively.
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URGENT help needed please...

I have been having problems with this problem...it says...
A graph of the Lissajous figure is given by the paraetric equations:

x=sin2t and y=cost

Show that the curve has two tangents at the point (0,0) and find their equations

Can someone please help me? I've been trying to figure this out for the past two days. I got the slope to be

-sint/cos(2t)*2 I am not sure where to go from there...so please..if anyone can help that would be fantastic. :confused:
 
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anyone...??
 
Origin means x=y=0. They are zero for t = pi/2 and -pi/2. For these you get two values of the slope, 1/2 and -1/2.


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