Eccentric anomaly <-> True Anomaly

$$ cos(\nu) = { cos(E)-e \over 1-ecos(E) } $$

$$ cos(E) = {e+cos(\nu) \over 1+ecos(\nu)} $$

Eccentric Anomaly -> True Anomaly

$$ tan({\nu \over 2}) = \sqrt{1+e \over 1-e} tan({E \over 2})$$

Trigonometric Fundamentals

$$ cos^2(\alpha)+sin^2(\alpha) = 1 $$

$$ tan({\alpha \over 2}) = {1-cos(\alpha) \over sin(\alpha)} = {sin(\alpha) \over 1+cos(\alpha)} $$

$$ cos(\alpha) = cos^2({\alpha \over 2}) - sin^2({\alpha \over 2}) = 2 cos^2({\alpha \over 2}) - 1$$