** Trigonometry** is a part of mathematics in which it studies about triangles, mainly **right triangles**. Trigonometry deals with relationships between the
angles and sides of triangles and also with the trigonometric functions. Here, we are study about the **trigonometry quadrants.**

** **

**There are four types of trigonometry quadrants available in trigonometry.**

- Quadrant I is from 0 to 90 degrees = 0 to p/2 radians
- Quadrant II is from 90 to 180 degrees = p/2 to p radians
- Quadrant III is from 180 to 270 degrees = p to 3p/2 radians
- Quadrant IV is from 270 to 360 degrees = 3p/2 to 2p radians

Where p = 3.14 rounded to 2 decimal places.

**Example 1:** Find sin (273^{o}).

** Solution:**

Sin (273) = sin (270 + 3)

= sin (270) cos (3) + cos (270) sin (3)

= (-1)cos(3)

= - 0.989

**Example 2:** Find the angle ‘a’ if sin (a) = -0.026551154 and cos (a) = -0.999647456

**Solution:**

Here, the sine is (+)ve and the cosine is (-)ve, we know the angle is in quadrant II which means the angle is between 90^{o} and 180^{o}.

sin** **(a) = -0.026551154 and cos (a) =
-0.999647456

a = Sin -1(-0.026551154) and a = cos -1(-0.999647456)

a= 66 and a = 66

Sin** **(66) = -0.026551154 and cos (66) = -0.999647456, and cos(114) =-0.999647456.

sin(114) = sin(180 - 66)

= sin(180)cos(66) - cos(180)sin(66)

= 0*cos(66) - (-1)*sin(66)

= sin(66)

Since sin (114) = sin (66), our angle is 114^{o}

**Example3:** What is the sign (+ or - ?) of:

A. cos 105°

b. sin 40°

c. csc 310°

Do these without calculator.

**Solution:**

a. Negative (100 degrees is in the second quadrant)

b. Positive (first quadrant - all are positive)

c. Negative (310 degrees is in the 4th quadrant)

**Example4** : What is the sign (+ or -) of

a) sec (-25°)

c) cos(185°)

**Solution:**

a. Positive (-25 degrees is in the 4th quadrant, since negative angles are measured clockwise.)

c. Negative (185 degrees is in the 3rd quadrant, and cos is negative there.