# How to Solve Coterminal Angles and Reference Angles? (+FREE Worksheet!)

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.

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

Find positive and negative coterminal angles to angle $$65^\circ$$.

Solution:

$$65^\circ-360^\circ=-295^\circ$$
$$65^\circ+360^\circ=425^\circ$$
$$-295^\circ$$ and a $$425^\circ$$ are coterminal with a $$65^\circ$$.

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

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

Solution:

$$\frac{π}{2}+2π=\frac {π+(2 ×2π) } {2} =\frac {π+4 π }{2}= \frac{5π}{2}$$
$$\frac{π}{2}-2π= \frac {π-(2 ×2π) } {2} =\frac {π-4 π }{2}= -\frac{3π}{2 }$$

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

Find positive and 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 positive and negative coterminal angles to angle $$\frac{π}{4}$$.

Solution:

$$\frac{π}{4}+2π= \frac {π+(4 ×2π) } {4} =\frac {π+8π }{4} =\frac{9π}{4 }$$
$$\frac{π}{4}-2π= \frac {π-(4 ×2π) } {4} =\frac {π-8 π }{4} =-\frac{7π}{4 }$$

## Exercises for Solving Coterminal Angles and Reference Angles

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

• $$\color{blue}{\frac{14π}{5}=} \\$$
• $$\color{blue}{-\frac{16π}{9}=} \\$$
• $$\color{blue}{\frac{41π}{18}=} \\$$
• $$\color{blue}{-\frac{19π}{12}=}$$
• $$\color{blue}{\frac{4π}{5}} \\$$
• $$\color{blue}{\frac{2π}{9}} \\$$
• $$\color{blue}{\frac{5π}{18}} \\$$
• $$\color{blue}{\frac{5π}{12}}$$

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