Exercise $1-$ Tangent line$($s$)$ to a $($parametric$)$ curve

$(1)$ Find an equation of the tangent to the parametric curve at the point corresponding to the given value of the parameter.

$($a$){}_1(t)=(1+4t-t^2,2-t^3),t=1,$

$($b$){}_2(t)=(tcos(t),tsin(t)),t=.$

$(2)$ Finds the points on the curve where the tangent is horizontal or vertical.

$($a$){}_3(t)=(t^3-3t,t^5-5t^4),$tinR,

$($b$){}_4(t)=(2cos(t),sin(2t)),$tin$[0,4].$