Question

Find parametric equations for the tangent line at the point (cos(3pi/6),sin(3pi/6), (3pi/6))

on the curve x=cost, y= sint, z=t
x(t)=?
y(t)=?
z(t)=?

Answer 1

`r(t)=(cos(t),sin(t),t) \\r'(t)=(-sin(t),cos(t),1) \\t= (3\pi)/(6) = (\pi)/(2) \\ r'(t)=(-\sin{(\pi)/(2)},\cos{(\pi)/(2)},1) \\ r'(t)=(-1,0,1) \\ \\x=0+t(-1)=-t \\y=1+t* 0=1 \\z= (\pi)/(2) +t`