each curve represents the motion of a particle moving in R2

x(t) = (2cos t, 3sin t) , 0 <= t <= 2Pi

x(t) = (3 sec t, 2 tan t) , (-1/3)pi <= t <= (1/3)pi

can someone sketch both these curves showing the direction of motion for me???

and find the velocity and speed of each of the particles with a step by step explanation

the speed of the first one i got as:

sqrt ( 4(sin t)^2 + 6 (cos t)^2 )

is there any way to further simplify this or should i leave it like this???

i also have to locate the points (x,y) where the velocity is horizontal, vertical or 0

i think this means when the derivative or x-component is 0, when derivative or y-component is 0, and when both are zero?

am i correct?

and can you list those points for both equations as well so i can verify them