Radians and Reference values

Question

How are radian measures more versatile than degree measures? How can reference angles help to quickly identify trig function values?

Answer 1

Radians are easier to use when it comes time to measure arc lengths (the distance between two points in the edge of a circle of, say, radius R); The radian measure of the angle that reaches these two points from the center, multiplied by R, is the linear distance of the arc.

Reference angles were more useful before everyone had a calculator on their phones. It allows you to memorize the coordinates of the sin, cos, and tan on the unit circle for some often used angles between 0 and 90deg (pi/2), like 30 deg, 45 deg and 60 deg (pi/6, pi/4, pi/3). After that, using the reference angles for these values, it's an easy step to find the sign of each. BTW, knowing the coordinates of 37 and 53 degrees is also helpful.