# Answer the following: Find the trigonometric functions of : 225° - Mathematics and Statistics

Diagram
Sum

Find the trigonometric functions of :

225°

#### 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 3rd 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
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q II. (1) c. | Page 33