I currently have a translated sine graph with the following formula:
$$\left(\sin\left(\frac{x}{50 / \pi} - \frac{\pi}{2}\right) + 1\right) \cdot 0.5$$
Which makes a graph like this
However I need to have the amplitude range between $0.2$ and $1.0$. Is there any way I can do this, while keeping the mentioned range as a variable, such as changing the min and max range at will?
Very easy to construct, $\sin$ goes from $-1$ to $+1$ so you just shift and stretch: $$f(x)=\text{min}+\frac12(\text{max}-\text{min})(1+\sin (kx+\phi))$$ or, if you prefer $$f(x)=\text{average} + \text{amplitude}\cdot \sin (kx+\phi)$$ where average=(max+min)/2 and amplitude = (max-min)/2.