Intense math (sin/cos)?

I am trying to make a nice number tween service. Like so.

for a=from,to do
set.Rotation=from+1
wait()
end 

I want to be able to have the number start slowly, speed up, and slow down before stopping.

I like the curve but I want to be able to start with a custom number, curve, and stop at the final number in a transition.

My brain hurts after attempting to Google this question.

Like this..

Graph!

Where a would be the value to loop set the rotation of the gui? and (0,from) would be the start and (1,to) would be the end.

What you're asking for is indeed a sine wave. sin(x) starts at 0, accelerates up to half the square root of 2 and then decelerates up to 1 over the domain of pi/2 radians (90 degrees).

The simplest solution is to use sin(x) from 0 to 90 degrees as a multiplier to tween from a to b.

Say the gui is rotated 45 degrees and you want it to go to 90:

local from=45
local to=90

local sin,rad=math.sin,math.rad
for i = 0, 90 do
	set.Rotation = from + sin(rad(i))*(to - from)
	wait()
end