engage vs sign up

engage

verb
  • To guarantee or promise (to do something). 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

sign up

verb
  • To agree to purchase some good or service. 

  • To add one's own name to the list of people who are participating in something (including amateur, but not professional, teams) 

  • To add a name to the list of people who are participating in something. 

How often have the words engage and sign up occurred in a corpus of books? (source: Google Ngram Viewer )