# 1.16: Coterminal Angles

**At Grade**Created by: CK-12

**Practice**Coterminal Angles

While playing a game with friends, you use a spinner that looks like this:

As you can see, the angle that the spinner makes with the horizontal is

### Coterminal Angles

Consider the angle

Now consider the angle

Notice that **co-terminal**. Not only are these two angles co-terminal, but there are infinitely many angles that are co-terminal with these two angles. For example, if we rotate another

#### Identifying Co-Terminal Angles

For the following questions, determine if the angle is co-terminal with

1.

No, it is not co-terminal with

2.

Yes,

3.

Yes,

### Examples

#### Example 1

Earlier, you were asked if it is possible to represent the angle any other way.

You can either think of

#### Example 2

Find a coterminal angle to

A coterminal angle would be an angle that is at the same terminal place as

#### Example 3

Find a coterminal angle to

A coterminal angle would be an angle that is at the same terminal place as

#### Example 4

Find two coterminal angles to

Rotating once around the circle gives a coterminal angle of

### Review

- Is
315∘ co-terminal with−45∘ ? - Is
90∘ co-terminal with−90∘ ? - Is
350∘ co-terminal with−370∘ ? - Is
15∘ co-terminal with1095∘ ? - Is
85∘ co-terminal with1880∘ ?

For each diagram, name the angle in 3 ways. At least one way should use negative degrees.

- Name the angle of the 8 on a standard clock two different ways.
- Name the angle of the 11 on a standard clock two different ways.
- Name the angle of the 4 on a standard clock two different ways.
- Explain how to determine whether or not two angles are co-terminal.
- How many rotations is
4680∘ ?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.16.

### Notes/Highlights Having trouble? Report an issue.

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Term | Definition |
---|---|

Coterminal Angles |
A set of coterminal angles are angles with the same terminal side but expressed differently, such as a different number of complete rotations around the unit circle or angles being expressed as positive versus negative angle measurements. |

### Image Attributions

Here you'll learn how to identify coterminal angles.

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