I'm having trouble creating my own trig function

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Adriane
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I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can help, I'd be extremely grateful. I can create my own graph and make my own additional problems if I just knew how to create the equation. My teacher gave us a lot of freedom on this, and I guess I'm just a little lost.
 

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The orbit of Neptune, like the other planets in the solar system, is an ellipse. Do you know how to express the equation for an ellipse in terms of sines and cosines? Have you studied polar coordinates yet by chance?