Section 12.1 Activig Derivatives of Parametric Curves 1. Consider the equation x2 + y2 =1, which gives the unit circle. Assume that x = f (t) and y = g(t) give the coordinates of (x, y) on the curve and represent the position of a \"zombie bee's\" path that has surmised to the parasitic bee disease. Assume that trepresents units of time since the time measurement has started and x and y represent the position (in cm from the center of the path). Assume the orientation of the path is clockwise. (a) Graph the bee's path in the coordinate plane. (b) What is the position of the bee when t= 5% seconds? (c) Determine how fast the bee is moving when t = 5?\" seconds. Problem 1 continued: (d) Determine the equation of the tangent line of the bee's path when t= - 4 7t seconds. 2. Consider the parametric equations x = tan(2t) dy y =-212 + 3t-1' Determine dx 3. Consider the parametric equations x = cost + sint y = sint -t cost . Determine the equation of the tangent line to the parametric curve when t = - 3 7T 4