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 2^nd 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