Hi. I'd like to know whether is it possible to do the following, and if so, how...(and also, whether is it possible to solve similar problems)(adsbygoogle = window.adsbygoogle || []).push({});

I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes known angle with the positive x-axis.

Curve:

x = ( R-r )( cos([tex]\varphi[/tex]) - cos([tex]\theta[/tex]) ) + D cos([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )

y = ( R-r )( sin([tex]\varphi[/tex]) - sin([tex]\theta[/tex]) ) + D sin([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )

R, r and D are known constants.

Ray:

y = tan([tex]\beta[/tex]) x

[tex]\beta[/tex], [tex]\theta[/tex] and [tex]\varphi[/tex] are angles, [tex]\varphi[/tex] is my parameter, [tex]\theta[/tex] and [tex]\beta[/tex] are some variable angles.

I need to find the coordinates of the intersection of curve and the ray as a function of [tex]\theta[/tex] and [tex]\beta[/tex].

In short I want to know coordinates of intersection but without the parameter [tex]\varphi[/tex] in them.

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# Solving trigonometric system of equations

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