Question

draw the curve traced out by r(t) = <2cos(t), 2sin(t)> and its derivative of various 't' values.

CALCULUS III- Vector Valued Functions.

Answer 1

This is just a circle of radius 2. The first derivative is\[d \vec{r}/dt=<-2\sin(t), 2\cos (t)>\]The derivative at t=0 and t=pi/2 are shown in the drawing.