# Trigonometry : Angles in Different Quadrants

## Example Questions

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### Example Question #1 : Angles In Different Quadrants

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.

### Example Question #2 : Angles In Different Quadrants

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.

### Example Question #3 : Angles In Different Quadrants

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.

### Example Question #4 : Angles In Different Quadrants

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 .

### Example Question #1 : Angles In Different Quadrants

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.

### Example Question #6 : Angles In Different Quadrants

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.

### Example Question #7 : Angles In Different Quadrants

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.

### Example Question #3 : Angles In Different Quadrants

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.

### Example Question #2 : Angles In Different Quadrants

1st

4th

3rd

2nd

3rd

Explanation:

When we think of angles, we go clockwise from the positive x axis.

Thus, for negative angles, we go counterclockwise. Since each quadrant is defined by 90˚, we end up in the 3rd quadrant.

### Example Question #1 : Angles In Different Quadrants

Which of the following answers best represent ?