Question

Find the trigonometric function of :

60°

Answer 1

Angle of measure 60° :

Let m∠XOA = 60°

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 =  `1/2"OP"`

= `1/2(1)`

= `1/2`

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

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

= `sqrt(3)/2`

Since point P lies in the 1^st quadrant,

x > 0, y > 0

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

∴ P ≅ `(1/2, sqrt(3)/2)` 

sin 60° = `sqrt(3)/2`

cos 60° = x = `1/2`

tan 60° = `y/x = ((sqrt(3)/2))/((1/2)) = sqrt(3)`

cosec 60° = `1/y = (1)/((sqrt(3)/2)) = 2/sqrt(3)`

sec 60° = `1/x = (1)/((1/2)` = 2

cot 60° = `x/y = ((1/2))/((sqrt(3)/2)) = 1/sqrt(3)`