How did the inca make such precise calculations in astronomy, architectal engineering and mathmatics?

The Inca were able to make very precise calculations in astronomy, engineering and mathematics due to their use of quipu. A quipu is a recoding device made out of strings and used by a number of cultures in the Andean area. It consists of a number of strings that are tied into knots in a particular symbolic pattern. Quipu were also used to collect data, maintain records, collect census records and other types of organizational tasks.

the option which was not a function of missionaries in the northwest was the first one - they established posts for trading furs and other goods.

missionaries were sent around the world to spread religion and their knowledge and others - they were not merchants who sold furs and other goods.