If you want to learn how to solve coterminal angles and Reference angles problems, you are in the right place.

## Related Topics

- How to Evaluate Trigonometric Function
- How to Solve Angles and Angle Measure
- How to Find Missing Sides and Angles of a Right Triangle
- How to Solve Trig Ratios of General Angles

## Step by step guide to solve Coterminal Angles and Reference Angles Problems

- Coterminal angles are equal angles.
- To find a coterminal of an angle, add or subtract \(360\) degrees (or \(2π\) for radians) to the given angle.
- Reference angle is the smallest angle that you can make from the terminal side of an angle with the \(x\)-axis.

### Coterminal Angles and Reference Angles – Example 1:

Find a positive and a negative coterminal angles to angle \(65^\circ\).

**Solution**:

\(65^\circ-360^\circ=-295^\circ \)

\( 65^\circ+360^\circ=435^\circ \)

\( -295^\circ\) and a \(435^\circ\) are coterminal with a \(65^\circ\).

### Coterminal Angles and Reference Angles – Example 2:

Find a positive and negative coterminal angles to angle \(\frac{π}{2}\).

**Solution**:

\(\frac{π}{2}+2π=\frac{5π}{2} \)

\( \frac{π}{2}-2π=-\frac{3π}{2 }\)

### Coterminal Angles and Reference Angles – Example 3:

Find a positive and a negative coterminal angles to angle \(70^\circ\).

**Solution**:

\(70^\circ-360^\circ=-290^\circ \)

\(70^\circ+360^\circ=430^\circ \)

\( -290^\circ\) and a \(430^\circ\) are coterminal with a \(70^\circ\).

### Coterminal Angles and Reference Angles – Example 4:

Find a positive and a negative coterminal angles to angle \(\frac{π}{4}\).

**Solution:**

\(\frac{π}{4}+2π=\frac{9π}{4 }\)

\( \frac{π}{4}-2π=-\frac{7π}{4 }\)

## Exercises for Solving Coterminal Angles and Reference Angles

### Find a coterminal angle between \(0\) and \(2π\) for each given angle.

- \(\color{blue}{\frac{14π}{5}=} \\ \)
- \(\color{blue}{-\frac{16π}{9}=} \\ \)
- \(\color{blue}{\frac{13π}{18}=} \\ \)
- \(\color{blue}{\frac{19π}{12}=} \)

- \(\color{blue}{\frac{4π}{5}} \\ \)
- \(\color{blue}{\frac{2π}{9}} \\ \)
- \(\color{blue}{\frac{5π}{18}} \\ \)
- \(\color{blue}{\frac{5π}{12}}\)