Consider the vector function given below.
2t, 3 cos(t), 3 sin(t)
(a) Find the unit tangent and unit normal vectors T(t) and
(b) Use this formula to find the curvature.
3. Consider the parametric curve x = sin 2t, y = − cos 2t for
−π/4 ≤ t ≤ π/4.
(a) (2 pts) Find the Cartesian form of the curve.
(b) (3 pts) Sketch the curve. Label the starting point and
ending point, and draw an
arrow on the curve to indicate the direction of travel.
(c) (5 pts) Find an equation for the curve’s tangent line at the
(1 point) For the given position vectors r(t)r(t) compute the
unit tangent vector T(t)T(t) for the given value of tt .
A) Let r(t)=〈cos5t,sin5t〉
B) Let r(t)=〈t^2,t^3〉
C) Let r(t)=e^(5t)i+e^(−4t)j+tk