# 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

At the completion of this Concept, you'll know more than one way to represent this angle.

### Watch This

James Sousa Example: Determine if Two Angles are Coterminal

### Guidance

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

#### Example A

Is the following angle co-terminal with

**Solution:** No, it is not co-terminal with

#### Example B

Is the following angle co-terminal with

**Solution:**

#### Example C

Is the following angle co-terminal with

**Solution:** Yes,

### Vocabulary

**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.

### Guided Practice

1. Find a coterminal angle to

2. Find a coterminal angle to

3. Find two coterminal angles to

**Solutions:**

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

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

3. Rotating once around the circle gives a coterminal angle of

### Concept Problem Solution

You can either think of

### Practice

- 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∘ ?

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### Image Attributions

Here you'll learn how to identify coterminal angles.