**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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