Let x(t) = 2 cos(t) + cos(2t) and y(t) = 2 sin(t) – sin(2t). a) Plot the curve for t = = [0,6].
b) Find the equation for the tangent line at (-1,2). (You may need to use nsolve for this part and use the plot to pick a good guess)
c) Find all points where the curve has a vertical tangent line for t in the interval [O, 6].
(Hint: Be careful which t values you use when finding the point and make sure to verify that your t value makes sense. Many t values may look like possible answers, but they are not.)