QUADRANTS

Quadrants :

Let X′OX and YOY′ be two lines at right angles to each other as in the figure given below.

we call X′OX and YOY′ as x-axis and y-axis respectively.

XOY - First 

YOX - Second

X′OY′ - Third 

Y′OX - Fourth

Angle in standard position:

If the vertex of an angle is at O and its initial side lies along x-axis, then the angle is said to be in standard position.

Angle in a quadrant :

An angle is said to be in a particular quadrant, if the terminal side of the angle in standard position lies in that quad-rant.

To check whether the given angle lies in which quad-rant, first we have to check the following

0° ≤ θ ≤ 90° - 1st 

90° ≤ θ ≤ 180° - 2nd

90° ≤ θ ≤ 180° - 3rd

270° ≤ θ ≤ 360° - 4th

  • If the given angle < 360°, we can draw a picture to know that the angles lies in which quad-rant 
  • If the given angle > 360°, then we have to divide the given angle by 360 and draw the picture for the remaining angle.

Example 1 :

Find the quad-rant in which the terminal sides of the following angles lie. 

- 60°

Solution :

Since the given angle is negative we have to take clock wise direction.

The terminal side of - 60° lies 4th quad-rant.

Example 2 :

- 300°

Solution :

To find -300° lie in which quad-rant, we have to draw a picture. Since the given angle is negative we have to take clock wise direction.

The terminal side of - 300° lies 2nd quad-rant

Example 3 :

Find the quad-rant in which the terminal sides of the following angles lie. 

1295°

Solution :

To find 1295° lie in which quad-rant, we have to draw a picture.

The terminal side of -1295° lies 3rd quad-rant

Example 4 :

Find the quad-rant in which the terminal sides of the following angles lie. 

380°

Solution :

Since the angle 380° is greater than 360°, we have to divide it by 360 and take the remainder.

380 = 1 x 360 + 20

20° is between 0° and 90° the given angle lies in 1st quad-rant.

After having gone through the stuff given above, we hope that the students would have understood "quad-rant". 

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