vector functions?

Question

how do I calculate the position and tangent vector of

r(t) = (x(t), y(t)) = (0.5+cos(t), sin(t)+cos(t))

Answer 1

x(t)= 0.5+cos(t)
y(t) = sin(t)+cos(t) gives you the position
If you need f(x,y)=0 you must eliminate t
x-0.5 = cost
y-x+0.5=sin t
square and sum
(x-0.5)^2+(y-x+0.5)^2=1
The velocity vector is
(x´(t),y´(t)) = (-sin t,cos t -sin t )

In vector notation
v= -sin (t) *i + ( cos t -sin t) *k
where i and k are the unit vectors along x and y axis