1. The problem statement, all variables and given/known data Find a vector-valued function f that traces out the given curve in the indicated direction. (a) Counterclockwise (b) Clockwise. 4x2+9y2=36 2. Relevant equations x2+y2=r2 cos2t+sin2t=1 3. The attempt at a solution From what I can determine, this is an ellipse. I believe this is how the answer is found. 4x2/36+9y2/36=36/36 x2/9+y2/4=1 so cos2t+sin2t=1 and x2/9+y2/4=1 this means x=3cos(t) and y=2sin(t) to balance it equivalently, I think. putting that in component form, 3cos(t)i+2sin(t)j for counterclockwise and 3cos(t)i-2sin(t)j for clockwise That does equal the correct answer , but I am not sure if I got to it correctly. Can someone please review my work and let me know if I am approaching this correctly, I do not show anything in my notes or in my book on how to perform this kind of equation.