Edit: Thanks to those commenting, I fixed my issue and now have reached the below function, as I had aimed. My remaining question would be how I might describe this function. I have taken the function from (Function For Sine Wave Between Two Exponential Cuves) where they were tackling a similar problem, and I want to be able to describe what the function is doing, but I don't know if it is causing oscillation or using midpoints between the linear functions to inform the sine wave.
I've attached an image of the new function: New function
end edit
I'm trying to make a sinusoidal function that dilates as it progresses between two linear functions so that its peaks and troughs are always in contact with the linear functions. To do this I have worked with the function;$$\frac{y_{3}+y_{2}}{2}-\frac{y_{3}-y_{2}}{2}\sin x $$ where y_3 and y_2 are linear functions built on a series of points and I got this as a result: Multi-sinusoidal function?
I've called it a 'multi'-sinusoidal as it looks like the function has made varying sine waves, each that has a peak for one of my table data points. For example, the largest sine wave matches my greatest point's y value; 6.3, and there is also a sine wave for the smallest value; 4.8.
Is there any way I could merge these functions so that it is just one sine wave, or there other mathematical 'boundary' formulas that I could use to tell the sine wave to equal the value of the linear function point it corresponds to?
Thanks !!