Feb  3 18:05 2006 from Josh 
The capital sigma is a summation sign; it's shorthand for "Add all these 
things up.  The capital pi is the equivalent sign for multiplication 
(multiply all these things together).  These are related (in an oblique 
way) to the integral sign. 
  The integral of cos is indeed sin, but you'll note that the integral of  
sin in actually -cos, not cos. This is because indefinite integrals (which 
is what it sounds like you're doing) are "anti-derivatives", which is to 
say it undoes a derivative. 
  Derivatives have really nice geometric interpretation: they are the  
slope of the line tangent to the curve, at a particular point. So, graph a 
straight line like y=x, and it's derivative; you will see the nice line of 
slope 1 (which is to say that it "goes up 1 every time it goes over to the 
right by 1"), which goes through the origin.  The derivative is just a 
constant function, y=1, because the slope of the line is 1 everywhere. 
 sin, cos and tangent also have a nice geometric interpretation: Look at a 
 right triangle.  The sin of an angle on this triangle is defined as the 
length of the leg opposite side from the angle over the length of the 
hypotenuse.  cos is the length of the adjacent leg over the length of the 
hypotenuse.  Sin and cos are bounded (by 1) because of the Pythagorean 
theorem (note that no side of the right triangle is longer than the 
hypotenuse).