Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Handling branch cuts in trig functions
Posted:
Mar 24, 2013 4:35 AM


I tried to simplify sqrt( sec(x)^2 ) but Mathematica will only do this by assuming x is inside one branch, say x>Pi/2 && x<Pi/2 but Maple and maxima simplified it but they gave the answer is terms of sec(x) to take care of the sign which depends on the branch.
Here is plot of sec(x)
http://mathworld.wolfram.com/Secant.html
 In[37]:= Assuming[x>Pi/2&&x<Pi/2,Simplify[Sqrt[Sec[x]^2]]] Out[37]= Sec[x]
In[39]:= Assuming[x > Pi/2 && x < Pi, Simplify[Sqrt[Sec[x]^2]]] Out[39]= Sec[x] 
If I just tell M that x>0, it will not simplify it.
 In[38]:= Assuming[x>0,Simplify[Sqrt[Sec[x]^2]]] Out[38]= Sqrt[Sec[x]^2] 
but Maple did it only with the x>0 assumption:
 restart; simplify(sqrt(sec(x)^2)) assuming x::positive;
1  cos(x) restart; simplify(sqrt(sec(x)^2)); / 1 \ csgn \cos(x)/  cos(x) 
On maxima 12.04.0
sqrt(sec(x)^2); sec(x)
I think now that answer to sqrt(sec(x)^2) should be sec(x) without need to give the branch. Since the only different is the sign. Or is there something else here?
Nasser



