Prepare for Quadrants

Four Quadrants

The word Quadrant comes form quad meaning four. For example, four babies born at one birth are called quadruplets, and a four-legged animal is a quadruped.

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (−,+), III (−,−), and IV (+,−). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.


As we know there are six trignometric ratios there signs depends on this quadrants there are four quadrants in total namely first quadrant, second quadrant,third quadrant, fourth quadrant. so here we will see what is first quadrant.

The range of angles varies from 00 to 3600 .In a plane with a system of cartesian coordinates, the sign of  x  and y coordinate decides the type of  quadrant.

The sign of this trignometric ratios depends on the quadrant in which the terminal side of the angle lies.

quadrant

In first quadrant,

x>0,y>0

Range of angle is- 00 to 900

So, all  trignometric ratios are positive.

In Second quadrant,

x<0,y>0

Range of angle is -  900 to 1800

So, sin and cosec are positive and the rest four cos , tan, sec, cot are negative.

In third quadrant,

x<0,y<0

Range of angle is - 1800 to 2700

So, tan and cot are positive and the rest others are negative.

In fourth quadrant,

x>0,y<0

Range of angle is -  2700 to 3600

So, cos and sec are positive and the rest others are negative.

Tabular representation of quadrants

Quadrant X
(horizontal) Y
(vertical) Example
I Positive Positive (3,2)
II Negative Positive (-3,2)
III Negative Negative (-2,-1)
IV Positive Negative (2,-1)


Application of quadrants:

As we know that the value of trignometric ratios depends upon the sign of x and y  coordinates which is different for different quadrants, so if we know the quadrant in which the x and y lies we can compute the sign of trignometric ratio accordingly. And we can solve various trignometric equations too.