Inverse of function so that it gives t instead of x?

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1

Hello everyone! I am making some tweening functions but I have encountered a specific formula that I do not know how to inverse. I presume that arcsin is involved but I do not know how exactly.

What my goal is, is to invert this formula so it returns t instead of x:

x = math.sin(math.pi/2*t-math.pi/2)+1

t = ...

Does anyone know how to do this? I am not that familiar with sin so I do not know how to invert it exactly.

Any help is appreciated!

2 
t = (2/math.pi) * math.asin(x - 1) + 1

You can use sites like Wolfram alpha to verify this type of question. Also it is worth noting that you will be limited to values of t within a certain range due to the periodic nature of the original equation.

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Here’s the steps involved in case anyone was interested.

x = math.sin(((math.pi/2)*t)-(math.pi/2))+1 --Subtract one from both sides.
x-1 = math.sin(((math.pi/2)*t)-(math.pi/2)) --Perform inverse of sine (arcsine) on both sides.
math.asin(x-1) = ((math.pi/2)*t)-(math.pi/2) --Add (math.pi/2) to both sides.
math.asin(x-1)+(math.pi/2) = (math.pi/2) * t --Divide both sides by (math.pi/2).
math.asin(x-1)*(1/(math.pi/2))+1 = t --Simplify stacked division.
math.asin(x-1)*(2/math.pi)+1 = t
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