Aberration of Light: Understanding Transformation Equations for Coordinates

[BareFootKing]

Homework Statement

http://s22.postimg.org/5vp0p2aox/Untitled.png

Homework Equations

The Attempt at a Solution

Here is the solution

I understand everything that must be done after one find the correct transformations for the two coordinates, but I don't understand why the transformation for y' has a minus R at the end. I would think y' = the first two terms x¬0cos + y¬0sin

 

[mfb]

What is ¬?

The last term comes from the squaring of [highlight]+[/highlight] y₀sin(wt) [highlight]-[/highlight] R

 

[BareFootKing]

Sorry, the" ¬" of "y¬0" was not suppose to be there. I was typing my post on word and copied and pasted it to the forum. I meant I thought that y' = x_ocos(wt) + y_osin(wt). Why is there a minus R term for y' and not for x'. I understand if it had the R term and we squared y' and x' and add them up and take the square root we would get the numerator shown in the final answer. But I didn't understand why y' had the minus R term in the begging.

 

[mfb]

Ah, that R.
At the considered point in time, you are at (0,R), so you have to subtract this R to get to the origin again.