pg. 732, #35 (moderate)
Sketch the plane curve r(t) = <cos(t),
sin(t)> ,find r'(t) and sketch the position vector r(t) and the
tangent vector r'(t) for t = Pi/4
Solution:
The curve <cos(t), sin(t)> is a circle. This is the vector
graph, which consists of vectors drawn
from the origin to the point (cos(t), sin(t)) :
The position vector and the tangent vector at t = Pi/4, sketched against a
circle look like this:
The complete graph of the velocity vectors gives a better picture of the
motion:
