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

Prove that the equations [itex]x=acos(\theta)[/itex] and [itex]y=bcos(\theta +\delta )[/itex] is the equation of an ellipse and what angle does this ellipse's major axis make with the x axis?

2. Relevant equations

Equation of an ellipse is [itex]x=acos\theta, y=asin\theta[/itex]

Rotation matrix is for a rotation by [itex]\psi[/itex] is [tex]A=\begin{pmatrix} cos\psi & -sin\psi \\ sin\psi & cos\psi \end{pmatrix}[/tex]

3. The attempt at a solution

I know the special case of [itex]\delta = \pi/2[/itex] is easy but I cannot do it for arbitrary [itex]\delta[/itex]. I worked out what an ellipse whose major axis forms an angle [itex]\psi[/itex] with the x axis looks like. I did this by applying a rotation matrix to the standard equation [itex]x=acos\theta, y=bsin\theta[/itex]

This gives [itex]x= acos\theta cos\psi - bsin\theta sin\psi[/itex] and [itex]y= acos\theta sin\psi + bsin\theta cos\psi [/itex]

Now, what is the relation between [itex]\psi[/itex] and [itex]\delta[/itex] in general. And I need to show that the equations [itex]x=acos(\theta)[/itex] and [itex]y=bcos(\theta +\delta )[/itex] can be brought to the same form as [itex]x= acos\theta cos\psi - bsin\theta sin\psi[/itex] and [itex]y= acos\theta sin\psi + bsin\theta cos\psi [/itex]

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# Help with ellipse geometry

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