6. Shown at right is the circle x + y? = r . The trigonometric operations are defined as follows. (x, y) COS & = sin 0 = tan 0 = seco = - CSCO = - cote = a) Draw a picture similar to the one drawn here. Instead of radius r, use radius 1. Show cos 0, sin 0, tan 0, sec@, csco, and cote as distances on your picture. (You will need to add some lines.) If you have drawn it correctly, you should be able to easily visualize the three Pythagorean identities. sin 0 + cos-0 = 1 tan 0 + 1 = sec- 0 cot' 0 + 1 = csc2 0 b) Use your knowledge of the derivatives of sin x and cos x, along with any number of derivative shortcut rules, to demonstrate the derivatives of tan x , sec x, csc x, and cotx. c) For each of the three identities shown in part a, differentiate both sides with respect to 0 and simplify. If differentiated correctly, each of the resulting equations should be obviously true