I came across the sentence, "I rejoice to hear it," and wasn't exactly sure how to read it. So I looked up "rejoice to hear," and found it again in a poem by Isaac Watts:
How did my heart rejoice to hear
My friends devoutly say,
"In Zion let us all appear,
And keep the solemn day!"
Does my original sentence, "I rejoice to hear it," mean, I rejoice at having heard it, or I rejoice to hear it -- I rejoice so that I may hear it.