The ellipse $$x^2/4^2+y^2/7^2=1$$
can be drawn with parametric equations. Assume the curve is traced clockwise as the parameter increases.
If $$x=4\cos t$$
Find $y$
Clearly this is a parametrization we can relate to the identity $\cos^2x+\sin^2x=1$, so the answer should be $y=7\sin t$. This gives then
$$\frac{x^2}{4^2}+\frac{y^2}{7^2}=1=\frac{4^2\cos^2}{4^2}+\frac{7^2\sin^2}{7^2}=1$$
But this is wrong, although it seems so apparently natural. I suspect it has to do with the direction. What is the error here?
Thanks!