Quadrant

The axes of the two-dimensional cartesian system divide the plane into four regions. The four regions are called quadrants. The plane is divided into equal parts. The quadrant is denoted by the roman numbers first quadrant (I), second quadrant (II), third quadrant (III), and the fourth quadrant (IV). The x-axis and the y-axis are divided into four regions. They contain positive and negative values of x and y.  The point where the two lines intersect each other is said to be the reference point or the origin.  All the measurement is taken on the basis of this reference point. It is considered as the starting point in the coordinate system. It has the value x = 0 and y = 0 that is the coordinates at that point is (0,0).


Quadrants in the Coordinate Plane

The plane is divided into four regions and the regions are classified as,

  1. First quadrant

  2. Second quadrant

  3. Third quadrant

  4. Fourth quadrant.

Now we will understand these quadrants in detail. The quadrant is always considered in the anti-clockwise direction (moves in the opposite side of the clockwise direction).


First Quadrant (I)

In the first quadrant, we have a positive x-axis and positive y-axis.  x and y both values are positive in this quadrant. In this quadrant, the angle measure starts from 0 degrees to 90 degrees. It is in the shape of a right angle.


Second Quadrant (II)

In the second quadrant, we have a negative x-axis and the positive y-axis. In this quadrant, x value will be negative and y value will be positive. In this quadrant, the angle measures from 90 degrees to 180 degrees.


Third Quadrant (III)

In the third quadrant, we have a negative x-axis and a negative y-axis. Both x and y values in this quadrant are negative. The angle measures from 180 degrees to 270 degrees in this quadrant.


Fourth Quadrant (IV)

In this quadrant, we have a positive x-axis and a negative y-axis. The x value is positive and the value is negative in this quadrant. The angle measures from 270 degrees to 360 degrees.

(image will be uploaded soon)


Quadrants

X - Coordinate

Y - Coordinate

1st Quadrant

Positive

Positive

2nd Quadrant

Negative

Positive

3rd Quadrant

Negative

Negative

4th Quadrant

Positive

Negative


Trigonometric Values in a Different Quadrant

The trigonometric values of the quadrant are given as follows.


The sine function according to the sine graph will have positive values in the first quadrant and the second quadrant and will have negative values in the third quadrant and the fourth quadrant. Cosec function will have similar values to the sine function.


The cosine function according to the cosine graph will have positive values in the first quadrant and the fourth quadrant will have negative values in the second quadrant and the third quadrant. The Sec function will have similar values to the cosine function.


The tangent function according to the tan graph will have positive values in the first quadrant and the third quadrant will have negative values in the second quadrant and the fourth quadrant. The cot function will have similar values to the tan function.


Trick to Remember

Add Sugar To Coffee where A= All, S = Sin/cosec  T = tan/cot, C= cos/sec thus all are positive in 1st quadrant only sin/cosec is positive in 2nd quadrant, tan/cot is only positive in 3rd quadrant and cos/sec is only positive in 4th quadrant.

FAQ (Frequently Asked Questions)

1.Elaborate on Plotting of Points in the Quadrants of the Graph.

Answer: There are some important steps that are useful in plotting the graph. They are given below,

  1. The first step is we need to draw the x-axis and the y-axis.

  2. The x-axis should be horizontal and the y-axis should be vertical.

  3. Consider the point of intersection (where both axes met) as the origin (0,0).

  4. The value on the origin is (0,0) because here the x-axis value is 0 and the y-axis value is also 0.

  5. To find the position value on the x-axis we first need to find the location on the y-axis.

  6. We will plot this point on the graph.

  7. Then we get one point on the graph of (3,5) and the other point we have is (0,0).

  8. The next step is to join these points by drawing a line.

  9. By following these steps, the graph is plotted on the x-axis and the y-axis.