Sketch the curve whose vector equation is Solution r t 2 cos

Last updated: 6/16/2023

Sketch the curve whose vector equation is Solution r t 2 cos t i 2 sin t j 5tk The parametric equations for this curve are y 2 sin t z X Since x y 4 sin t the curve must lie on the circular cylinder x y The point x y z lies directly above the point x y 0 which moves counterclockwise around the circle x y in the xy plane The projection of the curve onto the xy plane has vector equation r t 2 cos t 2 sin t 0 See this exampl Since z 5t the curve spirals upward around the cylinder as t increases The curve shown in the figure below is called a helix 2 0 0 0 2 57