I have been trying to solve some equations, and for the same I found an online answer. Here's the link - http://citeseerx.ist.psu.edu/viewdoc/downloaddoi=10.1.1.456.6096&rep=rep1&type=pdf#page=4
Since, I do not have problem with the whole part, I inserted a screenshot of the part I have problem understanding. This part is quite independent of the rest of the working, so I don't think anyone would have to check out the whole thing (honestly the whole thing is huge).
I do not understand why do we need to do -sx ?
Also, if my RHS had -2cost instead of 2cost and -3sint instead of 3sint (basically it was negative), would my sx still vary?
And just in case you wanna check the things before it:
I am really confused, and I really need to understand this part. Thank you for your time and help!!
Actually I think some of the part above that you cut out does matter. But my best answer based on what you showed is that the formula you have for $s_x$ (which you don't show) gives a value between $0$ and $\pi$. So if we know that $t$ and $s$ must be in the same quadrant, which we do, and we know that $\pi<t\leq2\pi$, then the formula for $s$ will give a value in the upper half plane and $t$ will be in the lower half. Thus they're not in the same quadrant. Thus we find the corresponding value of $s$ (via symmetry) that puts it in the same quadrant as $t$, that is $2\pi-s$. Now the formulas saying they're in the same quadrant can be valid.