Quadrants in the Coordinate Plane
The plane is divided into four regions and the regions are classified as,
-
First quadrant
-
Second quadrant
-
Third quadrant
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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.
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|
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.