Coterminal Angles and Reference Angles

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.

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

Related to "Coterminal Angles and Reference Angles"

Top 10 Grade 4 Common Core Math Practice Questions
Top 10 Grade 4 Common Core Math Practice Questions
Grade 8 ACT Aspire Math Worksheets
Grade 8 ACT Aspire Math Worksheets
Top 10 Grade 4 STAAR Math Practice Questions
Top 10 Grade 4 STAAR Math Practice Questions
Grade 8 MEAP Math Worksheets
Grade 8 MEAP Math Worksheets
Top 10 Grade 8 STAAR Math Practice Questions
Top 10 Grade 8 STAAR Math Practice Questions
Grade 8 MAP Math Worksheets
Grade 8 MAP Math Worksheets
Top 10 ALEKS Math Practice Questions
Top 10 ALEKS Math Practice Questions
Grade 8 NYSE Math Worksheets
Grade 8 NYSE Math Worksheets
Top 10 ATI TEAS 6 Math Practice Questions
Top 10 ATI TEAS 6 Math Practice Questions
Grade 8 OST Math Worksheets
Grade 8 OST Math Worksheets

Leave a Reply

Your email address will not be published. Required fields are marked *