Evaluate multivariable function [closed]

Question

I'm trying to use Mathematica to evaluate many values of $f(x,y) $, like $f(-\pi,\pi) $ for

$$f(x,y) = \left( \frac{-1}{4}\sin \left( \frac{x-y}{2} \right)\sin y \right)\left( \frac{-5}{4}\sin \left( \frac{x-y}{2} \right)\sin y-\cos \left( \frac{x-y}{2} \right)\cos y \right) \\-\frac{1}{4}\left( \sin \left( \frac{x-y}{2} \right)\sin y+\cos \left( \frac{x-y}{2} \right)\cos y \right).$$

So I input :

f[x_, y_] := ((-1/4) sin[(x - y/2)] sin[y]) 
             ((5/4) sin[(x - y/2)] sin[y] - (-1/4) cos[(x - y/2)] cos[y]) 
             - (1/4) (sin[(x - y/2)] sin[y] + cos[(x - y/2)] cos[y])

and

f[-\[Pi], \[Pi]]

Mathematica then outputs :

1/4 (-cos[-((3 \[Pi])/2)] cos[\[Pi]] - 
    sin[-((3 \[Pi])/2)] sin[\[Pi]]) - 
 1/4 sin[-((3 \[Pi])/
    2)] sin[\[Pi]] (1/4 cos[-((3 \[Pi])/2)] cos[\[Pi]] + 
    5/4 sin[-((3 \[Pi])/2)] sin[\[Pi]])

But I want my final answer to be a number. Why didn't Mathematica evaluate the trigonometric functions? Thank you.

Answer 1

It works for me on V 9

f[x_, y_] := ((-1/4) Sin[(x - y/2)] Sin[y]) ((5/4) Sin[(x - y/2)] Sin[y] - 
             (-1/4) Cos[(x - y/2)] Cos[y]) - (1/4) (Sin[(x - y/2)] Sin[y] + 
             Cos[(x - y/2)] Cos[y])

In[45]:= f[-Pi, Pi]
Out[45]= 0

(ps. it helped to write Sin instead of sin and Cos instead of cos :)

Mathematica's commands, symbols and functions start with UpperCase. You are on the right track of using lowerCase, but you should do that for your own variables and symbols, not for what is meant to be Mathematica's own.

 Length[Names["System`*"]]
 (*4573*)

 Length@Cases[UpperCaseQ[#] & /@ StringTake[Names["System`*"], 1], True]
 (*4377*)

But almost all those which are not UpperCase are actually these strange symbols and they do not really count:

So you can see, that Mathematica uses UpperCase first letter for its own use, which is a good thing.