please also attach workings

thank you

2. A particle is moving according to the parametric curve r : (g, g) > R2 dened by r(t) = (1 tan2(t)))i + (tan(t) tan3(t))j. (a) In WebWork Problem 2, you calculated r(0), r'(0), r(%),r'(),r(%) and r'(%). Find r( ,r'( , r(%) and r'(%). You may want to use the fact that tan2(t) and sec2(t) are even functions while tan(t) and tan3(t) are odd functions. (b) Plot each of the velocity vectors r'(t) you found in WebWork Problem 2 and part (b) on a single diagram. In each case, base the vector at r(t). (c) Use the velocity vectors you plotted on your diagram in (b) to plot the path range(r) indicating the direction of motion with arrows. You may assume that E c r(t) is approximated by the curve 3; = |3:| 2 for tvalues near g E u r(t) is approximated by the curve 3; = |m| 2 for tvalues near . where x