Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

Find the trigonometric functions of : −225° - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Find the trigonometric functions of :

−225°

Advertisement Remove all ads

Solution

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 2nd 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

Concept: Trigonometric Functions of Specific Angles
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×