Question

Find the trigonometric functions of 120°.

Answer 1

Let m∠XOA = 120°

Its terminal arm (ray OA) intersects the standard unit circle in P (x, y). 

Draw seg PM perpendicular to the X-axis.

Δ OMP is a 30° - 60° - 90° triangle

OP = 1

PM = `sqrt3/2`OP

`= sqrt3/2(1)`

`= sqrt3/2`

OM = `1/2` OP

`= 1/2 (1)`

`= 1/2`

Since point P lies in the 2^nd quadrant, x < 0, y > 0

∴ x = - OM = `- 1/2` and y = PM = `sqrt3/2`

∴ P ≡ `((-1)/2, sqrt3/2)`

sin 120° = y = `sqrt3/2`

cos 120° = x = `- 1/2`

tan 120° = `y/x = (sqrt3/2)/(-1/2) = - sqrt3`

cosec 120° = `1/y = 1/(sqrt3/2) = 2/sqrt3`

sec 120° = `1/x = 1/(- 1/2)` = - 2

cot 120° = `x/y = (-1/2)/(sqrt3/2) = - 1/sqrt3`