Faking arcsin.....

Andy Long, Spring 2024

Now that we have a good fake for sine, it seems like we might have a good fake for arcsin:

Plot[{Sin[x],ArcSin[x],x},{x,-Pi/2,Pi/2},PlotRange->All,AspectRatio->1,PlotStyle->{Black,Blue,Dashed}]

p1=Plot[{Sin[x],ArcSin[x],x},{x,0,Pi/2},PlotRange->All,AspectRatio->1,PlotStyle->{Black,Blue,Dashed}]

Arcsine is the inverse of sine... ;

x0=0.99
arcSinner[x_]:=Solve[Sin[y]==x,y] 
y0=y/.arcSinner[x0][[1]]
p2=ListPlot[{{x0,y0},{y0,x0}}];
Show[p1,p2]