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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
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