How to Solve Coterminal Angles and Reference Angles

How to Solve 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.

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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 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.

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

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