A very easy way to do this AND bypass the trig functions would be to use vectors. First thing you would want to do is calculate the differences in x-position and y-position of the red dot and the cursor:
var dx:Number = _root._xmouse - _root.red._x;
var dy:Number = _root._ymouse - _root.red._y;
The numbers above are then the respective x and y components of a vector from the red dot to the cursor. The next step is to normalize the vector. First calculate the magnitude of the vector (the distance formula):
var mag:Number = Math.sqrt((dx * dx) + (dy * dy));
Then you divide each component of your vector by it's magnitude:
var x:Number = dx/mag;
var y:Number = dy/mag;
Now you have a unit vector (a vector with a length of one) that points in the direction of the cursor from the red dot. Now you simply just multiply each component of the direction vector by a speed constant that you set to set the projectiles velocity:
var SPEED_CONST:Number = 5;
var xspeed:Number = x * SPEED_CONST;
var yspeed:Number = y * SPEED_CONST;
And that's all there is to it. For further reading on normalizing vectors go here: Normalizing Vectors
For further reading on vectors in general, check this out: Vectors
Hope this helps you out, and if you have any questions feel free to ask! Good luck