c++ - I am looking to create realistic car movement using vectors

I have goggled how to do this and found this http://www.helixsoft.nl/articles/circle/sincos.htm I have had a go at it but most of the functions that were showed didn't work I just got errors because they didn't exist. I have looked at the cos and sin functions but don't understand how to use them or how to get the car movement working correctly using vectors. I have no code because I am not sure what to do sorry.

Any help is appreciated.

EDIT:

I have restrictions that I must use the TL engine for my game, I am not allowed to add any sort of physics engine. It must be programmed in c++. Here is a sample of what i got from trying to follow what was done in the link I provided.

if(myEngine->KeyHeld(Key_W))
    {

        length += carSpeedIncrement;
    }
    if(myEngine->KeyHeld(Key_S))
    {
        length -= carSpeedIncrement;
    }
    if(myEngine->KeyHeld(Key_A))
    {
        angle -= carSpeedIncrement;
    }

    if(myEngine->KeyHeld(Key_D))
    {
        angle += carSpeedIncrement;
    }

    carVolocityX = cos(angle);
    carVolocityZ = cos(angle);

    car->MoveX(carVolocityX * frameTime);
    car->MoveZ(carVolocityZ * frameTime);