Find all the angles that are coterminal with the given angle. (Let k be an arbitrary integer.)
Transcribed Image Text:**Title: Finding Coterminal Angles**
**Introduction**
In this lesson, we will explore how to find all angles that are coterminal with a given angle. Coterminal angles are angles that share the same initial and terminal sides but differ in the measures by full rotations (multiples of 360°).
**Problem Statement**
Find all angles that are coterminal with the given angle. (Let \( k \) be an arbitrary integer.)
Given Angle: \(-225^\circ\)
**Explanation of the Concept**
An angle \( \theta \) is coterminal with another angle \( \alpha\) if they differ by an integer multiple of \( 360^\circ \). Mathematically, this can be written as:
\[ \alpha = \theta + 360^\circ \times k \]
Where:
- \( \alpha \) is any angle coterminal with \(\theta\).
- \( \theta \) is the given angle.
- \( k \) is any integer.
**Solution**
Given angle, \(\theta = -225^\circ\). We need to find all angles coterminal with \(-225^\circ\).
Using the coterminal angle formula:
\[ \alpha = -225^\circ + 360^\circ \times k \]
Therefore, the angles coterminal with \(-225^\circ\) are:
\[ \alpha = -225^\circ + 360^\circ k \]
Where \( k \) is any integer.
**Conclusion**
By substituting different integer values for \( k \), you can generate an infinite number of angles that are coterminal with \(-225^\circ\).
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
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![**Title: Finding Coterminal Angles**
**Introduction**
In this lesson, we will explore how to find all angles that are coterminal with a given angle. Coterminal angles are angles that share the same initial and terminal sides but differ in the measures by full rotations (multiples of 360°).
**Problem Statement**
Find all angles that are coterminal with the given angle. (Let \( k \) be an arbitrary integer.)
Given Angle: \(-225^\circ\)
**Explanation of the Concept**
An angle \( \theta \) is coterminal with another angle \( \alpha\) if they differ by an integer multiple of \( 360^\circ \). Mathematically, this can be written as:
\[ \alpha = \theta + 360^\circ \times k \]
Where:
- \( \alpha \) is any angle coterminal with \(\theta\).
- \( \theta \) is the given angle.
- \( k \) is any integer.
**Solution**
Given angle, \(\theta = -225^\circ\). We need to find all angles coterminal with \(-225^\circ\).
Using the coterminal angle formula:
\[ \alpha = -225^\circ + 360^\circ \times k \]
Therefore, the angles coterminal with \(-225^\circ\) are:
\[ \alpha = -225^\circ + 360^\circ k \]
Where \( k \) is any integer.
**Conclusion**
By substituting different integer values for \( k \), you can generate an infinite number of angles that are coterminal with \(-225^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643de4d0-ca3c-47ed-94f6-02fd3fafa065%2F69233569-fe67-44fa-9dc4-138131d4fc96%2F403nf0b.jpeg&w=3840&q=75)
