Can a player tap Junk Tokens without paying the other costs?

Let’s say a player has The Millennium Calendar on the battlefield. This card’s ability triggers when one or more permanents that player controls are untapped.

Let’s also say that player has a surplus of Junk Tokens. Junk Tokens have a tap ability, but must be sacrificed to fully activate their ability. Can that player simply tap the Junk Tokens, not pay the rest of the Junk Tokens’ cost (sacrificing them) so the tokens remain on the battlefield for The Millennium Calendar trigger?