Question

The parametric curve described by the equations x=\cos(t),\;\;y=\sin(t)\cos(t) has two tangent lines at (0, 0). find the equations of these tangent lines. list them in order of increasing slope.

Answer 1

Hello,


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