You'll need a numerical method to solve this equation for
Hello Again,
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I've been doing some stuff on this problem using excel. What I did was get values for t and solve for x then graph so as x was the x-axis and t the y-axis. This produced a function as shown in the first below graph (labelled original). The equation of this curve is the answer to my question however I do not know how to determine what its equation is. As seen using a linear approximation the gradient of the line is essentially: t=x. The actual equation is therefore actually modeled by: y=mx+c+k; where c=0, m=1, x=x and y=t: t=x+k. Therefore I figured in order to determine the actual equation of the curve I needed to find K. [k=t-x] Graphing this (K=y-axis and x=x-axis) gave the "New" function. I figured that K would be a simple sine function which I know how to regress the equation of visually, however as seen the function ("new" in the below image), is a skewed function. I have had no experience at all in determining the equation of a skewed sine function. So my question is:
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Could someone please tell me how I would go about determining the equation of the "New" function in the below graph?
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[First Graph]
[Graph of "New" from first graph]
Any help would be greatly appreciated.
Thanks,
Z.C.