I am finding the tangent at the point $\theta$ when $x = a\cos(\theta), y = b\sin(\theta)$
The tangent is calculated with the following $$\frac{y-f(\theta)}{x-\theta}=f'(\theta)$$ at a point where $x=\theta$ and $y = f(\theta)$;
I have attempted the following:
$$\cos^{-1}(\frac{x}{a})=\theta, y = b\sin(\cos^{-1}(\frac{x}{a}))$$
Then this gives me the following: $$\frac{y-b\sin(\cos^{-1}(\frac{x}{a}))}{x-a}=$$
However, this does not look like the correct approach to me.
I have instead attempted dividing $x$ over $y$ but cannot seem to find the solution. The expected solution is $x\cos(\theta/a)+y\sin(\theta/b)=1$.