Transposing SIN(RADIANS())

Does anyone know the transposition for this in excel if A,B,C are known to get X ... A=B*SIN(RADIANS(X))+C
fyi I have spent many hours on this before joining the forum.
Thanks in advance for anyone who gives it a go.

A=B*SIN(X)+C (I took out the conversion to radians, because it is not necessary for the algebra.
Subtract C from both sides: A-C=B*SIN(X)
Divide by B: (A-C)/B=SIN(X)
The inverse function for SIN() is the arcsin (ASIN() in Excel), so take the ASIN() of both sides: ASIN((A-C)/B)=X (x is in radians at this point).

Edit to add: Remember from trig that the standard convention for the ASIN() function is to return the angle from the 1st and 4th quadrants (angle between -pi/2 and +pi/2). If you need angles from the 2nd and 3rd quadrants, you will need further testing to return the correct angle.

I tried your solution but maybe I am not implementing it as you intended, I included my worksheet in case the quadrant issue mentioned is preventing me from getting the result I need.

I will have to look at this closer later, but I think we will need to know all of the reasons why 269.6303... (-90.369694...) is the only correct answer for this and why -89.63030... (270.369694...) is not. You are correct that the problem is in choosing which quadrant the result should be in. Your solution is from the 3rd quadrant, where, as I noted earler, the ASIN() will return the result from the 4th quadrant. How do you know that the answer is in the 3rd quadrant?

I only need a hemisphere from 90 degrees to 270 degrees so I only have one point generated by the x500 intersection with the arc ... which I found by trial and error to be at 269.630305934 degrees giving me the result at exactly the 500th data point in the range my data is generated at .25 degree increments

Center X,1221304.534 Y,19467.67358
Radius 1220829.947

269.5 X,521.0720288 Y,8814.057706
269.75 X,486.2079865 Y,14140.81494
270 X,474.5865653 Y,19467.67358


I only have a corresponding degree for X 269.5 - 521.0720288 and 269.75 - 486.2079865, either sides of 500 ... so the answer has to be between these numbers and 269.630305934 is in between and correct, range is generated by the .25 degree steps but am looking for degree value at 500 X or any other whole number of X ... Y can easily be calculated after from the newly obtained degree result for X.

So all of your results will be in the 2nd and 3rd quadrants, is that right? To get the 2nd/3rd quadrant results from the 1st/4th quadrant, simply subtract the 1st/4th quadrant result from 180. 180-ASIN(...).

That should solve the problem. If you stick around and I stick around, I might also look at solving this problem using complex numbers (and Excel's IM...() functions) or how to rewrite it so it becomes an inverse tangent function (where you can use the ATAN2() function, which works better for full circle stuff.