Question

Find the trigonometric functions of 225°.

Answer 1

Angle of measure 225° :

Let m∠XOA = 225°

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 45° – 45° – 90° triangle.

OP = 1

OM = `1/sqrt(2)"OP"`

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

= `1/sqrt(2)`

PM = `1/sqrt(2)"OP"`

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

= `1/sqrt(2)`

Since point P lies in the 3^rd quadrant,

x < 0, y < 0

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

∴ P ≡ `(-1/sqrt(2), - 1/sqrt(2))`

sin 225° = y = `-1/sqrt(2)`

cos 225° = x = `- 1/sqrt(2)`

tan 225° = `y/x = (-1/sqrt(2))/(-1/sqrt(2))` = 1

cosec 225° = `1/y = 1/(-1/sqrt(2)) = -sqrt(2)`

sec 225° = `1/x = 1/(-1/sqrt(2)) = -sqrt(2)`

cot 225° = `x/y = (-1/sqrt(2))/(-1/sqrt(2))` = 1