Because just find and proceed.
Consider the space curve given by the equation
r(t)=t^2i +[sin(2t)-2tcos(2t)]j+[cos(2t)+2tsin(2t)]k
(a) Find the unit tangent vector T(t) and the equation of the tangent line at t=Pi.
Everytime I attempt this problem I end up with the most despicable derivatives. I have tried to use trigonometric identities to clean up the problem I'm trying to solve a bit but it still leads to unatural results (a huge repetitive derivative computation). Is there some trigonometric identity that I'm missing out on or a trick that could produce results that make sense?
Yeah I know, but when I try to compute the unit tangent vector r'(t)/[r'(t)] the result I get for the derivative and when I try to make this derivative the magnitude is beyond disgusting. Is there some trigonometric identity involved or a trick? The most obvious one is cos^2(2t)+sin^2(2t)=1.