how to find coterminal 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.

Coterminal Angles and Reference Angles – Example 1:

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

Solution:

\(65^\circ-360^\circ=-295^\circ \)
\( 65^\circ+360^\circ=435^\circ \)
\( -295^\circ\) and a \(435^\circ\) are coterminal with a \(65^\circ\).

Coterminal Angles and Reference Angles – Example 2:

Find a positive and negative coterminal angle 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 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:

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

Exercises for Solving Coterminal Angles and Reference Angles

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

\(\color{blue}{\frac{14π}{5}=} \\ \)
\(\color{blue}{-\frac{16π}{9}=} \\ \)
\(\color{blue}{\frac{41π}{18}=} \\ \)
\(\color{blue}{-\frac{19π}{12}=} \)

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

Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.

1 month ago