Question

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

Answer 1

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.