Question

consider the parametric equations.
x=4cost
y=5sint
-pi/2
9 years ago

Answer 1

eliminate the parametric to find Cartesian equation of the curve


i got x^2/16 + y^2 /25 = 1 but how would i graph it with the arrows ?

Answer 2

start at \(-\frac{\pi}{2}\) or rather that point

Answer 3

oh when you graph it like the direction of the curve

Answer 4

which i think is \((0,-5)\)

Answer 5

then go counter clockwise

Answer 6

not sure you go all the way around though

Answer 7

hmm how you know its counterclockwise ?

Answer 8

cause that is the positive direction, and you are going from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\)
HOWEVER

Answer 9

i think you only get half the ellipse

Answer 10

ohh

Answer 11

actually now that i look at it that was a lousy answer i gave
you know it goes that way because as \(t\) increases from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) , \(y=4\sin(t)\) increases from \(-4\) to \(4\)

Answer 12

ok from -5 to 5 really but you get the idea

Answer 13

and \(x=4\cos(t)\) goes from 0 to 1 and back to 0

Answer 14

but you don't go all the way around the ellipse, since you only have half the period for sine and cosine

Answer 15

ohh k