Question

Find the trigonometric functions of :

330°

Answer 1

Trigonometric Functions of 330° :

Let measure of ∠XOA in standard position be 330°.

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

Draw segment PM perpendicular to the X-axis.

∴ ΔOMP is a 30° – 60° – 90° triangle.

Op = 1.

OM = `sqrt(3)/2"OP"`

= `sqrt(3)/2(1)`

= `sqrt(3)/2`

PM = `1/2"OP"`

= `1/2(1)`

= `1/2`

Since point P lies in the 4^th quadrant,

x > 0, y < 0

∴ x = OM = `sqrt(3)/2 and y = -"PM" = -1/2`

∴ P ≡ `(sqrt(3)/2, (-1)/2)`

sin 330° = y = `-1/2`

cos 330° = x = `sqrt(3)/2`

tan 330° = `y/x = (-1/2)/(sqrt(3)/2) = -1/sqrt(3)`

cosec 330° = `1/y = 1/((-1/2))` = – 2

sec 330° = `1/x = 1/((sqrt(3)/2)) = 2/sqrt(3)`

cot 330° = `x/y = (sqrt(3)/2)/(-1/2) = -sqrt(3)`