Angles in Different Quadrants

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Trigonometry › Angles in Different Quadrants

Questions 1 - 10
1

Which quadrant does belong?

II

III

IV

I

Explanation

Step 1: Define the quadrants and the angles that go in:

QI:

QII:

QIII:

QIV:

Step 2: Find the quadrant where is:

The angle is located in QII (Quadrant II)

2

Determine the quadrant that contains the terminal side of an angle measuring .

Explanation

Each quadrant represents a change in radians. Therefore, an angle of radians would pass through quadrants , , and end in quadrant . The movement of the angle is in the clockwise direction because it is negative.

3

Determine the quadrant that contains the terminal side of an angle .

Explanation

Each quadrant represents a change in degrees. Therefore, an angle of radians would pass through quadrants , , , and end in quadrant . The movement of the angle is in the clockwise direction because it is negative.

4

What quadrant contains the terminal side of the angle ?

Explanation

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between and , the angle is a third quadrant angle. Since is between and , it is a thrid quadrant angle.

5

What quadrant contains the terminal side of the angle ?

Explanation

First we can convert it to degrees:

The movement of the angle is clockwise because it is negative. So we should start passing through quadrant . Since is between and , it ends in the quadrant .

6

What quadrant contains the terminal side of the angle ?

Explanation

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a first quadrant angle. Since is between and , it is a first quadrant angle.

7

What quadrant contains the terminal side of the angle ?

Explanation

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a second quadrant angle. Since is between and , it is a second quadrant angle.

8

What quadrant contains the terminal side of the angle ?

Explanation

First we can convert it to degrees:

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a third quadrant angle. Since is between and , it is a third quadrant angle.

9

Which of the following angles lies in the second quadrant?

Explanation

The second quadrant contains angles between and , plus those with additional multiples of . The angle is, after subtracting , is simply , which puts it in the second quadrant.

10

What quadrant contains the terminal side of the angle ?

Explanation

First we can write:

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between and , the angle is a second quadrant angle. Since is between and , it is a second quadrant angle.

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