Consider the curve, $C,$ deteremined $by$ the vector valued function vec$(r)(t)=($:$sin(2t),t,cos(2t)$:$)on$

the interval $0,2and$ the point $P=(0,,1)on$ the curve.

$(i)$ Sketch the curve.

$(ii)$ Determine the length $of$ the curve.

$(iii)$ Determine the curvature $of$ the curve $Cat$ the point $P$

$(iv)$ Find the unit tangent vector, vec$(T)$ and unit normal vector vec$(N)atP.$

$(v)$ Find the center and radius $of$ the circle $of$ curvature for the curve $Cat$ the point $P.$