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.
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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.
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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.
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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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