S., Try giving him attention before he whines: i.e. as soon as he gets up, give him on-on-one attention for 5 minutes: tell him that you'll play with him, read to him, and then when you are finished you want him to play by himself while you get breakfast ready for everyone. Do the same at dinner time, and two other times of the day.
When you are with him, be REALLY PRESENT for him. Give him eye contact often during this time, as well as during the entire day. Whining, annoying as it is, is his way of asking you to be connected with him. If you can think of it that way, some of your annoyance will melt away (which makes it easier for you).
That's not to say that you should accept whining; he needs to learn not to whine. Tell him that whining hurts your ears and "If you want my attention, say 'Mommy, I want to talk to you please.'" And that you will NOT respond when he whines. And then follow through with it. Make up a sign to use rather than using words to remind him if he is whining (cover your ears, or something similar, and go back to what you were doing). When he speaks to you without whining, drop what you are doing and listen with your FULL attention for a minute and go back to work. And you can ask him if he wants to join you in cooking, etc. and explain what you are doing as you do it--like you're running a cooking show! Children are so interested in learning about the world around them; it's difficult to watch everything happening yet not to be involved. If you remember that your child may be whining because he WANTS TO LEARN and be part of things, some of the annoyance to his whining can go away.
Scheduling more time to do all of your tasks is essential; that's the hardest part of parenting, to go at a slower pace so our children can be included. But it is our most important job: our children depend upon us to teach them about the world.
So, give him quality attention frequently throughout the day, include him in your tasks, and re-frame your thinking about his whining (that's to help YOU feel a little less annoyed). Hope this helps. G.