Question

Find the trigonometric function of :

30°

Answer 1

Angle of measure 30°:

Let m∠XOA = 30°

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

Draw seg 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 1^st quadrant,

x > 0, y > 0

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

∴ P = `(sqrt(3)/2, 1/2)`

sin 30° = y = `1/2`

cos 30° = x = `sqrt(3)/2`

tan 30° = `y/x = (1/2)/(sqrt(3)/2) = 1/sqrt(3)`

cosec 30° = `1/y = 1/((1/2))` = 2

sec 30° = `1/x=1/(((sqrt3)/2))=2/sqrt3`

cot 30° = `x/y = (sqrt(3)/2)/(1/2)=sqrt3`