how does five degrees east of north keep a plain going north when the wind pushes the plain four point six degrees west of north?

This is not calculus. It is a vector problem. THe wind is pushing the plane west.

If you need the solution, to find the direction of the wind, a comination of law of sines and law of cosines will be needed. I cannot assist here, it is too complicated without a diagram.

Ok Thank you.

You're welcome! If you have any other questions, feel free to ask.