Question

Find the coterminal angles for 8pi/3.
I found one:
8pi/3 - 2pi= 2pi/3

My textbook says that I should add subtract 4pi to find the other one and I'm very confused as to how you know what to add/ subtract.

Answer 1

A standard rotation is 2π.
So whatever angle you have either adding or subracting multiples of 2π will yield a coterminal angle.
e.g
8π/3 -----> think 480°
8π/2 - 2π = 2π/3 -----> think 120°
8π/3 + 2π = 14π/3 -----> think 840°
8π/3 - 4π = -4π/3 -----> think -240°
8π/3 + 12π = 44π/3 -----> think 2640°

now use your calculator and find sin or any other trig function of thos angles, you will get the same answer.

If you wanted only those angles -2π ≤ Ø ≤ 2π
you would have -4π/3 and 2π/3