Find the Distance Traveled by a Particle with Position $( x , y ) = \left( \cos ^ { 2 } t , \cos t \right)$

Essay

Find the distance traveled by a particle with position $( x , y ) = \left( \cos ^ { 2 } t , \cos t \right)$ as t varies in the time interval $[ 0,4 \pi ]$ . Compare with the length of the curve.