Spent ages looking at this, Just realised the problem. On line 75 you are using x in the calculation of the y-value, but the x value was changed the line before. try something like this:

double length = sqrt( x*x + y*y );
x /= length; // same as x = x / length but easier to type
y /= length;

Simples, I have made this mistake many times
In your append function, you constantly set temp_1 to the next value. But eventually the next value will be null. Even so, temp_1 becomes null and you try and access its variables, then kablooey.
try changing the check to:

while( temp_1-> next != null )

All the maths functions use radians I believe, so try something like this

//Somewhere at the top
#define PI 3.14159

double degreesToRadians( double degrees )
{
  return ( degrees / 180 ) * PI
}

Like this:

return u1*u2 + v1*v2;

The method would be a little laborious if you are content with using the old functions ( also, for the c-stuff I meant getc instead of peek), but an example would be:

string s;
char c = getc(); // this removes the first character from the stream
                 // E.G the 'w' in "word", leaving "ord" in the stream
while( c != '\0' && c != ' ' ) // stop when stream ends or the word ends
{
  s += c; // add the character to the string you want
  c = getc(); // take the next character from the stream
}

After this, you could check whether c is a space, meaning that a number follows it, and use scanf to bring it in.

A more c++ approach would be easier, and could look along the lines of

string s;
int x = 0;
cin >> s; // add the first word to s, leaving either nothing or
          // the number
if( cin.peek() == ' ' ) //check whether there is a space following the word
{
  cin >> x; // input the number
}