# Maple : Is it really that hard to realize that sin(pi)=0 ?!

• May 29th 2010, 02:00 AM
Maple : Is it really that hard to realize that sin(pi)=0 ?!
I have an annoying problem in Maple.

I wanted maple to calculate the $10^th$ taylor series of f(x), while:

$f(x):=\frac{1}{2\pi}\int^{\pi}_0 e^{xcos(t)} dt$

and so I wrote :

f := (int(exp(x*cos(t)), t = 0 .. pi))/(2*pi)
p10 := taylor(f, x = 0, 11)

And I got an answer that involved multiplying by $sin(\pi)$. I must change all these into zeros, so I tried to use the 'subs' command, or to simplify, even 'simplify trig', but it didn't change a thing.

What can I do in order to get a simple answer?

Thank you :)
• May 29th 2010, 04:12 AM
TKHunny
The sine function is single-valued only in the Real world.

Try forcing Maple to assume that 'x' is Real. You should be able to do this with a Symbolic Modifier.
• May 29th 2010, 04:21 AM
Oh... and how can I make Maple assume that 'x' is a real symbol?
• May 29th 2010, 05:32 AM
TKHunny
There should be an "Assume" paremeter. Something like (assume,x=real)
• June 5th 2010, 06:40 PM
scorpion007
You have to use Pi not pi, because pi is just a symbol, whereas Pi is the constant 3.14...

Code:

sin(Pi);                                       0 sin(pi);                                   sin(pi)
Code:

f := (int(exp(x*cos(t)), t = 0 .. Pi))/(2*Pi);                         int(exp(x cos(t)), t = 0 .. Pi)                     f := -------------------------------                                       2 Pi              p10 := taylor(f, x = 0, 11);           1  1  2    1  4    1    6    1    8      1      10    / 11\   p10 := - + - x  + --- x  + ---- x  + ------ x  + -------- x  + O\x  /           2  8      128      4608      294912      29491200