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.

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

Related Topics

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.

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

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

How to Determine Limits Using the Squeeze Theorem?How to Determine Limits Using the Squeeze Theorem?
How to Determine Limits Using Algebraic Manipulation?How to Determine Limits Using Algebraic Manipulation?
How to Estimate Limit Values from the Graph?How to Estimate Limit Values from the Graph?
Properties of LimitsProperties of Limits
How to Find the Expected Value of a Random Variable?How to Find the Expected Value of a Random Variable?
How to Define Limits Analytically Using Correct Notation?How to Define Limits Analytically Using Correct Notation?
How to Solve Multiplication Rule for Probabilities?How to Solve Multiplication Rule for Probabilities?
How to Solve Venn Diagrams and the Addition Rule?How to Solve Venn Diagrams and the Addition Rule?
How to Find the Direction of Vectors?How to Find the Direction of Vectors?
Vectors IntroductionVectors Introduction

What people say about "How to Solve Coterminal Angles and Reference Angles? (+FREE Worksheet!)"?

No one replied yet.

Leave a Reply