I have to find the osculating circle of r(t) = <2cos(t),3sin(t)> at t = /2.
I find r'(t)=<-2sin(t),3cos(t)> and |r'(t)|=(4sin^2(t)+9cos^2(t))^(1/2). I converted that into |r'(t)| = (4 + 5cos^2(t))^(1/2). I am stuck on taking the derivative of the Unit Tangent vector to find the Principal Normal Unit vector in order to find the curvature. The derivative is getting horrible. Am I on the right track?