Sketch the curve whose vector equation is r(t) = 2 cos(t) 1+2 sin(0) 35. Solution The...

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Sketch the curve whose vector equation is r(t) = 2 cos(t) 1+2 sin(0) 35. Solution The parametric equations for this curte are y-2 sin(t), 2- ** Since y the curve must be on the circular cylinder The point (..) les directly above the point te,. y. 0), which moves counterclockwise around the circle the xy-plane (The projection of the curve onto the xy-plane has vector equation r(r) (2 costr), 2 sin(t) 0). See this example Since zst, the curve spirals upward around the cylinder as e increases. The curve, shown in the figure below, is caled a helix. sin(t)- (2,0,0) Sketch the curve whose vector equation is r(t) = 2 cos(t) 1+2 sin(0) 35. Solution The parametric equations for this curte are y-2 sin(t), 2- ** Since y the curve must be on the circular cylinder The point (..) les directly above the point te,. y. 0), which moves counterclockwise around the circle the xy-plane (The projection of the curve onto the xy-plane has vector equation r(r) (2 costr), 2 sin(t) 0). See this example Since zst, the curve spirals upward around the cylinder as e increases. The curve, shown in the figure below, is caled a helix. sin(t)- (2,0,0)