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Plot Question using Show[] function with different domain ranges

Posted 1 month ago
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My goal is to display the inverse trigonometric function of ArcCos and Cos through a specific x range of 0 to Pi for Cos and -1 to 1 for the ArcCos since those domain ranges will pass the horizontal line test as being one-to-one and thus inverses within that domain.

I do not have any problem plotting Cos and ArcCos individually as shown below in the following two plots - see attached.

However when I try to combine the two plots using the Show[] function, as displayed in the last plot, the results are far from desirable.

I have tried a bunch of different configurations and various options, but so far nothing has seemed to correct the problem so I decided to reach out to the community for help. Undoubtedly it is something that I am not doing correctly and I would appreciate someone in the community showing me the correct way of handling this sort of situation.


Mitch Sandlin


The Show command adopts the PlotRange from the first plot, which can be annoying. You can impose your own PlotRange that covers your whole range of interest:

Show[Plot[ArcCos[x], {x, -1, 1}], Plot[Cos[x], {x, 0, \[Pi]}], 
 PlotRange -> All, AspectRatio -> Automatic]
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