Find The Measure Of The Least Positive Angle That Is Coterminal With The Given Angle. 56 Degree

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Introduction

In trigonometry, angles are a fundamental concept that plays a crucial role in various mathematical operations. One of the essential topics in trigonometry is the concept of coterminal angles. A coterminal angle is an angle that has the same terminal side as another angle. In this article, we will explore the concept of coterminal angles, their properties, and how to find the measure of the least positive angle that is coterminal with a given angle.

What are Coterminal Angles?

Coterminal angles are angles that have the same terminal side. In other words, two angles are coterminal if they have the same initial and terminal points. For example, if we have an angle of 56 degrees, we can find a coterminal angle by adding or subtracting a full rotation (360 degrees) to the given angle.

Properties of Coterminal Angles

Coterminal angles have several properties that make them useful in trigonometry. Some of the key properties of coterminal angles include:

  • Same terminal side: Coterminal angles have the same terminal side.
  • Different initial points: Coterminal angles have different initial points.
  • Addition and subtraction: Coterminal angles can be found by adding or subtracting a full rotation (360 degrees) to the given angle.
  • Equivalence: Coterminal angles are equivalent in terms of their trigonometric functions.

Finding Coterminal Angles

To find the measure of the least positive angle that is coterminal with a given angle, we can use the following steps:

  1. Add or subtract a full rotation: Add or subtract a full rotation (360 degrees) to the given angle.
  2. Find the least positive angle: Find the least positive angle that is coterminal with the given angle.
  3. Check for equivalence: Check if the coterminal angle is equivalent to the given angle in terms of their trigonometric functions.

Example: Finding Coterminal Angles

Let's consider an example to find the measure of the least positive angle that is coterminal with a given angle.

Example 1: Finding Coterminal Angles

Find the measure of the least positive angle that is coterminal with the given angle of 56 degrees.

Step 1: Add a full rotation

Add a full rotation (360 degrees) to the given angle of 56 degrees.

56 + 360 = 416 degrees

Step 2: Find the least positive angle

Find the least positive angle that is coterminal with the given angle.

416 - 360 = 56 degrees

Step 3: Check for equivalence

Check if the coterminal angle is equivalent to the given angle in terms of their trigonometric functions.

Since the coterminal angle (56 degrees) is equivalent to the given angle (56 degrees), we can conclude that the measure of the least positive angle that is coterminal with the given angle of 56 degrees is 56 degrees.

Conclusion

In conclusion, coterminal angles are an essential concept in trigonometry that plays a crucial role in various mathematical operations. By understanding the properties and how to find coterminal angles, we can solve problems involving trigonometric functions and angles. In this article, we explored the concept of coterminal angles, their properties, and how to find the measure of the least positive angle that is coterminal with a given angle.

Frequently Asked Questions

Q: What is a coterminal angle?

A: A coterminal angle is an angle that has the same terminal side as another angle.

Q: How do I find the measure of the least positive angle that is coterminal with a given angle?

A: To find the measure of the least positive angle that is coterminal with a given angle, add or subtract a full rotation (360 degrees) to the given angle and find the least positive angle that is coterminal with the given angle.

Q: What are the properties of coterminal angles?

A: The properties of coterminal angles include the same terminal side, different initial points, addition and subtraction, and equivalence in terms of their trigonometric functions.

Q: How do I check if a coterminal angle is equivalent to the given angle?

A: To check if a coterminal angle is equivalent to the given angle, compare their trigonometric functions.

Glossary

  • Coterminal angle: An angle that has the same terminal side as another angle.
  • Terminal side: The side of an angle that is opposite the initial point.
  • Initial point: The starting point of an angle.
  • Full rotation: A rotation of 360 degrees.
  • Least positive angle: The smallest positive angle that is coterminal with a given angle.

References