Express y through R and x. How can I express y

shangokm

shangokm

Answered question

2022-01-26

Express y through R and x.
How can I express y through R and x?
y=R±R2(Rarccos(1±yR)x)2
It can be transformed into this :
y=±Rcos(2yRy2+xR)R

Answer & Explanation

tipoule137p

tipoule137p

Beginner2022-01-27Added 10 answers

You can't, because R and x don't determine y. For example, consider R=1,x=0, and if you plot the function cos(2yy2)1y you can see it has two solutions.
the second equation doesn't follow from the first. The plot of the first is this and it has two real solutions: maybe adding some conditions can help finding a closed formula for y. The correct second equation is y=R±Rcos(x±y2+2RyR), with the two ± independent from each other, the internal one coming from resolving a second degree equation.

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