Max/Min of a function using Lagrange Multipliers

[andrewjohnsc]

Homework Statement

Find the absolute maximum and minimum values for f(x,y) = sin x + cos y on the rectangle R defined by 0<=x<=2pi and 0<=y<=2pi using the method of Lagrange Multipliers.

The Attempt at a Solution

I don't know where to start in getting the constraint into something I can work with!

 

[benorin]

you can always use $$x+y=C$$ where $$C$$ is some constant.

 

[andrewjohnsc]

I don't understand how that constrains the function to 0<=x<=2pi 0<=y<=2pi