Consider the function r(t) = ln sin t i + t j, 0 < t < .

a. Roughly sketch the curve r(t) in the window -5 x 5, -1 y 5, using your calculator in parametric mode to help you. Show the orientation of the curve in your sketch. Make sure your calculator is in radian mode, not degree.

b. Calculate r(/6), and label the corresponding point P on your curve from part a.

c. Without doing any calculations, sketch the unit tangent vector T(/6) and principal unit normal vector N(/6) with their tails at point P on your sketch from part a.

d. Calculate T(/6), showing all work.

e. Find N(/6), doing as little additional work as possible. No explanation needed.

f. Interpreting r(t) as the position function of a particle, find the tangential component of the particle's acceleration at time t = /6. You can leave your answer exact or round to the nearest hundredth.