How would you find the exact value of the six trigonometric function of 120 degrees?

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Answer 1 · 2016-08-09T08:41:18

On the Cartesian Plane, an angle of 120° lies in the second quadrant.

Using the associated right-angled triangle with sides of length #-1,sqrt3 and 2# for the sides, x, y and r respectively,

the six trig ratios are defined as

#sin 120° = y/r = sqrt3/2 and "cosec" 120° = r/y = 2/sqrt3#

#cos 120° = x/r = (-1)/2 and sec 120° = 2/(-1)#

#tan 120° = y/x = sqrt3/(-1) and cot 120° = (-1)/sqrt3#

Notice that the three ratios on the right are reciprocals of the three on the left.