Treat it as the game it is! At the moment it's a game she's winning, so why should she quit? Your bright, beautiful daughter whines because it works, it's fun, it gives her power, and it gets a rise out of her Mama and Daddy. Two-year-olds say NO and throw things - remember? Whining is what four-year-olds do. It's part of their job description.
Do you have to play? No! You're the grown-up. You can make up a new game. You can inform her the whining game is over. Yes, you'll have to tell her, not just start in. Before that, however, figure out what will best make her decide that her game isn't worth playing. Loss of TV shows or dvds? Loss of time at the park or with friends? Decide the consequences of not coming to dinner without whining - eating in the kitchen by herself? If she whines during dinner, is dinner over? (She won't starve.) If she deliberately talks back to you - which is what she's doing when you tell her not to use that tone and she whines anyhow - what is the best consequence? I can't help you with this because I don't live at your house!
You'll have to give careful thought to this and stick to the game plan, no matter what; you may find it inconvenient at times, but look at it as important education for your daughter. It's SO much better to handle this now than let it slide until she's a dramatic, stubborn, whiny teen.
When she starts doing her drama bit, you want to act quickly with the consequence (that's why you need to have thought it out thoroughly first). Be friendly and firm, and don't use too many words! She doesn't need a lot of explanation; she needs to listen to Mama and do what Mama says - which, incidentally, is the new game. Doing it Mama's way gets smiles and hugs and a little (not overmuch) praise! "Oh, Mama has a better game after all (she thinks); my whining isn't so much fun any more."
Expect this to take time - she'll try to keep having her way, of course - and expect a somewhat bumpy road. To cheer *yourself* up, stop at your nearest library and find Betty McDonald's "Mrs. Piggle-Wiggle" books. Your daughter isn't old enough for them but you might get a good laugh out of 'em, and maybe you need one right now! There's one story about a girl who plays the game of "I'll do it because I want to but not because you tell me to," which is related to the one your daughter is playing.
(P.S. Just read through the other answers, and you've got some great ones! I'll underscore a point many of them have made: never give your daughter something she whines for. She should never get a reward out of her unacceptable behavior!)