Please show all work and formulas. Thank you!

12. Which of the following formulas would give the length of the outer loop for the curve: r =4+8sin(0) (Hint: Graph first!!) 7x/6 I. 2 V(4+8sin @)+(8cos0)-de 7x/6 II. J V(4+8sin @) +(8cos@)-de+ [ V(4+8sin @)2 +(8cos 0)-de 0 1 1x/6 7x/6 III. [ V(4+8sin @) +(8cos@)'d0+2 (4+8sin@) +(8cos 0)-de A) I only B) I and II only C) I and III only D) II and III only E) I, II and III. F) None of these