Adjusting a $y = \sin(x)$ graph slightly I have a function where
$$ y = m\sin\Bigl(\frac{x^{1.1}+30}{0.7d}\Bigr)^{2.2} $$
where $m = 45$ and $d = 120$ (constants)
I would like the turning point at the top of the sin curve to peak at 0.75d (90). I would like the starting and finishing values to remain the same.
The current function is plotted in blue. I would like a line similar to the red one. Feel free to ditch the sin function, if another method would be better

Thanks for any help.

Consider the curve $$y=\frac{(x-4)^4}{12}-\frac{kx^2}{2}+cx+d,$$ where the constants are given by $d=5-\frac{90^4}{12}$ and $$240=2×30^4-12k(120^2)+24(120c)+24d,\\2M=2d+180c-8100k,$$ with $M$ being the maximum value you want the function to attain.
