Are quadrants still used if so what for?

Answer 1

Quadrants and sextants are still used but to a much lesser degree since the introduction of electronic instruments and satellite GPS systems were introduced.

Quadrants/sextants are instruments used to measure angles in surveying and navigation.

Using trigonometry when surveying, measuring an angle and knowing the length of a side and another angle of a triangle other distances and angles can be calculated.

In navigation, measuring the angle of a star from the horizon and using a set of tables and an accurate time piece your position can be calculated.