Question

Find the trigonometric functions of :

−240°

Answer 1

Trigonometric Functions of ( – 240°) :

Let the measure of ∠XOA in standard position be − 240°.

Its terminal arm (ray OA) intersects the x· standard unit circle in P (x, y), which lies in the second quadrant.

Draw segment PM perpendicular to the X-axis.

Then OM =l x l and MP = l y l.

In right-angled triangle OMP,

m∠MOP = 60° and OP= 1

∴ m∠MPO = 30°

∴ OM = `1/2"OP" = 1/2 xx 1 = 1/2`

∴  y² = MP² = OP² − OM² 

= `1^2 - (1/2)^2`

= `1 - 1/4 = 3/4`

∴ y = `± sqrt(3)/2 and x = ± 1/2`

But P lies in the second quadrant.

∴ x < 0 and y > 0

∴ x = `-1/2 and y = sqrt(3)/2`

∴ P is `(-1/2, sqrt(3)/2)`

∴ sin (− 240°) = y = `sqrt(3)/2`

cos (− 240°)  = x = `-1/2`

tan (− 240°)  = `y/x = ((sqrt(3)/2))/((-(1)/2)) = -sqrt(3)`

cosec (− 240°)  = `1/y = 1/((sqrt(3)/2)) = 2/sqrt(3)`

sec (− 240°) = `1/x = 1/((-1/2))` = − 2

cot (− 240°) = `x/y = ((-(1)/2))/((sqrt(3)/2)) = -1/sqrt(3)`.