It is always the acute angle from the x axis that counts.
so you either use 180 or 360
1. sin 390
one complete revolution and 30 degrees more. That is just sin 30
2. sec(-1290)
1390/360 = 139/36 = 3 clockwise revolutions -210
-210 is equivalent to 360-210 = 150 which is in the second quad
180-150=30
sec = 1/cos and cos is negative in the second quad so so is sec
sec(-1290)= - sec(30)