(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

x^{2}+y^{2}=r^{2}

cos^{2}t+sin^{2}t=1

3. 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.

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# Homework Help: Vector-Valued Function Ellipse

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