The Inverse Cosine  arccos(z) .   Verify that the formula(s)   

(ii a)            ,  

(ii a)            .  

are correct.  (At least for values of z in the upper half plane  .)

Explore Formula (ii b).

Enter the formula     and explore.
Remark.  This might be the formula used in Mathematica's built in function  .

We can use Mathematica to verify the formula graphically, for values of z in the upper half plane  .  

Remark. If you mess around with the square root it will be wrong. A portion that is supposed to be in the fourth quadrant appears symmetrically in the second quadrant.

(c) 2006 John H. Mathews, Russell W. Howell