- #1

vandersmissen

- 19

- 0

## Homework Statement

Find a vector-valued function f that traces out the given curve in the indicated direction.

(a) Counterclockwise (b) Clockwise.

4x

^{2}+9y

^{2}=36

## Homework Equations

x

^{2}+y

^{2}=r

^{2}

cos

^{2}t+sin

^{2}t=1

## The Attempt at a Solution

From what I can determine, this is an ellipse. I believe this is how the answer is found.

4x

^{2}/36+9y

^{2}/36=36/36

x

^{2}/9+y

^{2}/4=1

so cos

^{2}t+sin

^{2}t=1 and x

^{2}/9+y

^{2}/4=1

this means x=3cos(t) and y=2sin(t) to balance it equivalently, I think.

putting that in component form, 3cos(t)i+2sin(t)j for counterclockwise and 3cos(t)i-2sin(t)j for clockwise

That does equal the correct answer , but I am not sure if I got to it correctly. Can someone please review my work and let me know if I am approaching this correctly, I do not show anything in my notes or in my book on how to perform this kind of equation.