### All Trigonometry Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 #2 : Angles In Different Quadrants

What quadrant contains the terminal side of the angle ?

**Possible Answers:**

**Correct answer:**

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 #5 : Angles In Different Quadrants

What quadrant contains the terminal side of the angle ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 #3 : Angles In Different Quadrants

What quadrant contains the terminal side of the angle ?

**Possible Answers:**

**Correct answer:**

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 #8 : Angles In Different Quadrants

Which of the following angles lies in the second quadrant?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #9 : Angles In Different Quadrants

What quadrant contains the terminal side of the angle ?

**Possible Answers:**

**Correct answer:**

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 #4 : Angles In Different Quadrants

In what quadrant does lie?

**Possible Answers:**

3rd

1st

2nd

What are quadrants?

4th

**Correct answer:**

3rd

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.

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