# Plotting a ArcCos function

I didn't manage to plot a simple function with ArcCos.

Plot[ArcCos[(x + 1)/Sqrt[x]], {x, -1, 1}]


With this function, the plot returned is empty.

Do you have some ideas for conducting this plotting ?

• For Power function I remember that to not have this problem I use Surd rather than Power. Is there a equivalent for inverse trigonometric functions ? Oct 15, 2015 at 9:19
• May be a stupid question but I would like to be sure. If I put Re do I obtain the same plot that I could obtain a Ti calc for example ? Oct 15, 2015 at 12:45

The function is complex-valued, try

Plot[Re[ArcCos[(x + 1)/Sqrt[x]]], {x, -1, 1}]

• Wouldn't be more instructive e.g. Plot[{Re @ #, Im @ #}& @ ArcCos[(x + 1)/Sqrt[x]], {x, -1, 1}, Evaluated -> True, PlotStyle -> Thick]? Oct 15, 2015 at 9:25
• Or Plot[ReIm@ArcCos[(x + 1)/Sqrt[x]], {x, -1, 1}, Evaluated -> True]
– user31001
Oct 15, 2015 at 10:16
• I try this : Plot[Re[ArcCos[(x + 1)/Sqrt[x]]], {x, -2, 2}] But my plot seems to be a bit strange ??? Oct 15, 2015 at 14:46

Whenever the square root of a complex number is used here, we choose the root with the positive real part (or positive imaginary part if the square was negative real).

$\arccos x=2 \arctan \frac{\sqrt{1-x^2}}{1+x}, if -1<x\le 1$

Plot[Im[2 ArcTan[Sqrt[-x^2 - x - 1]/Sqrt[x] + x + 1]], {x, -1, 1}]


The same for the real part:

 Plot[Re[2 ArcTan[Sqrt[-x^2 - x - 1]/Sqrt[x] + x + 1]], {x, -1, 1}]