You must know what reduction x angle is in each quadrant. x<90 degrees
1st quadrant ,x is less or equal to 90 degrees and all the trig functions are positive (sin, cos and tan)
2nd quad, x = 180-x , sine is positive and the other trig functions are negative
3rd quad, x = 180 + x , tan is positive and the other trig functions negative
4th quad, x = 360 - x, cos is positive and the other trig functions negative.
For example simplify tan 120 :
x angle will be 180 - 60 to give 120, so we have tan 120 = tan 60
but operation 180 - 60 (180-x) is in quadrant 2 where tan is negative, hence is correctly -tan 60