# Coterminal Angles and Reference Angles

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

## 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.

### 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 $$65^\circ$$.

### Example 2:

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

Solution:

$$\frac{π}{2}+2π=\frac{5π}{2}$$
$$\frac{π}{2}-2π=-\frac{3π}{2 }$$

### 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 $$70^\circ$$.

### 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

### Find a coterminal angle between $$0$$ and $$2π$$ for each given angle.

• $$\color{blue}{\frac{14π}{5}=} \\$$
• $$\color{blue}{-\frac{16π}{9}=} \\$$
• $$\color{blue}{\frac{13π}{18}=} \\$$
• $$\color{blue}{\frac{19π}{12}=}$$
• $$\color{blue}{\frac{4π}{5}} \\$$
• $$\color{blue}{\frac{2π}{9}} \\$$
• $$\color{blue}{\frac{5π}{18}} \\$$
• $$\color{blue}{\frac{5π}{12}}$$