Question

Find the trigonometric function of :

300°

Answer 1

Angle of measure 300°:

Let m∠XOA = 300°

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 4^th quadrant,

x > 0, y < 0

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

∴ P = `(1/2, (-sqrt(3))/2)`

sin 300° = y = `(-sqrt(3))/2`

cos 300° = x = `1/2`

tan 300° =  = `y/x = (-(sqrt(3))/2)/(1/2) = -sqrt(3)`

cosec 300° = `1/y = 1/((-(sqrt(3))/2)) = (-2/sqrt(3))`

sec 300° = `1/x = 1/((1/2))` = 2

cot 300° = `x/y = (1/2)/(-sqrt(3)/2) = -1/sqrt(3)`